Volume
LIPIcs, Volume 58
41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Mathematical Foundations of Computer Science (MFCS)
Event
MFCS 2016, August 22-26, 2016, Kraków, PolandEditors
Publication Details
- published at: 2016-08-19
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-016-3
- DBLP: db/conf/mfcs/mfcs2016
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Complete Volume
LIPIcs, Volume 58, MFCS'16, Complete Volume
Abstract
LIPIcs, Volume 58, MFCS'16, Complete Volume
Cite as
41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@Proceedings{faliszewski_et_al:LIPIcs.MFCS.2016,
title = {{LIPIcs, Volume 58, MFCS'16, Complete Volume}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016},
URN = {urn:nbn:de:0030-drops-65861},
doi = {10.4230/LIPIcs.MFCS.2016},
annote = {Keywords: Theory of Computation}
}
Document
Front Matter
Front Matter, Foreword, Conference Organization, External Reviewers, Table of Contents
Abstract
Front Matter, Foreword, Conference Organization, External Reviewers, Table of Contents
Cite as
41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{faliszewski_et_al:LIPIcs.MFCS.2016.0,
author = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
title = {{Front Matter, Foreword, Conference Organization, External Reviewers, Table of Contents}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {0:i--0:xvi},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.0},
URN = {urn:nbn:de:0030-drops-64225},
doi = {10.4230/LIPIcs.MFCS.2016.0},
annote = {Keywords: front matter, foreword, conference organization, external reviewers, table of contents}
}
Document
Invited Talk
How Far Are We From Having a Satisfactory Theory of Clustering? (Invited Talk)
Abstract
This is an overview of the invited talk delivered at the 41st International Symposium on Mathematical Foundations of Computer Science (MFCS-2016).
Cite as
Shai Ben-David. How Far Are We From Having a Satisfactory Theory of Clustering? (Invited Talk). In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{bendavid:LIPIcs.MFCS.2016.1,
author = {Ben-David, Shai},
title = {{How Far Are We From Having a Satisfactory Theory of Clustering?}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {1:1--1:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.1},
URN = {urn:nbn:de:0030-drops-65078},
doi = {10.4230/LIPIcs.MFCS.2016.1},
annote = {Keywords: clustering, theory, algorithm tuning, computational complexity}
}
Document
Invited Talk
Decidable Extensions of MSO (Invited Talk)
Abstract
This is an overview of the invited talk delivered at the 41st International Symposium on Mathematical Foundations of Computer Science (MFCS-2016).
Cite as
Mikolaj Bojanczyk. Decidable Extensions of MSO (Invited Talk). In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{bojanczyk:LIPIcs.MFCS.2016.2,
author = {Bojanczyk, Mikolaj},
title = {{Decidable Extensions of MSO}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {2:1--2:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.2},
URN = {urn:nbn:de:0030-drops-65089},
doi = {10.4230/LIPIcs.MFCS.2016.2},
annote = {Keywords: monadic second-order logic, extensions, decidability, automata}
}
Document
Invited Talk
Optimal Reachability in Weighted Timed Automata and Games (Invited Talk)
Abstract
This is an overview of the invited talk delivered at the 41st International Symposium on Mathematical Foundations of Computer Science (MFCS-2016).
Cite as
Patricia Bouyer-Decitre. Optimal Reachability in Weighted Timed Automata and Games (Invited Talk). In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 3:1-3:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{bouyerdecitre:LIPIcs.MFCS.2016.3,
author = {Bouyer-Decitre, Patricia},
title = {{Optimal Reachability in Weighted Timed Automata and Games}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {3:1--3:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.3},
URN = {urn:nbn:de:0030-drops-65090},
doi = {10.4230/LIPIcs.MFCS.2016.3},
annote = {Keywords: timed automata, model-checking, optimization}
}
Document
Invited Talk
Scale-Free Networks, Hyperbolic Geometry, and Efficient Algorithms (Invited Talk)
Abstract
The node degrees of large real-world networks often follow a power-law distribution. Such scale-free networks can be social networks, internet topologies, the web graph, power grids, or many other networks from literally hundreds of domains. The talk will introduce several mathematical models of scale-free networks (e.g. preferential attachment graphs, Chung-Lu graphs, hyperbolic random graphs) and analyze some of their properties (e.g. diameter, average distance, clustering). We then present several algorithms and distributed processes on and for these network models (e.g. rumor spreading, load balancing, de-anonymization, embedding) and discuss a number of open problems. The talk assumes no prior knowledge about scale-free networks, distributed computing or hyperbolic geometry.
Cite as
Tobias Friedrich. Scale-Free Networks, Hyperbolic Geometry, and Efficient Algorithms (Invited Talk). In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 4:1-4:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{friedrich:LIPIcs.MFCS.2016.4,
author = {Friedrich, Tobias},
title = {{Scale-Free Networks, Hyperbolic Geometry, and Efficient Algorithms}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {4:1--4:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.4},
URN = {urn:nbn:de:0030-drops-65106},
doi = {10.4230/LIPIcs.MFCS.2016.4},
annote = {Keywords: power-law graphs, scale-free graphs, random graphs, distributed algorithms}
}
Document
Invited Talk
RNA-Folding - From Hardness to Algorithms (Invited Talk)
Abstract
This is an overview of the invited talk delivered at the 41st International Symposium on Mathematical Foundations of Computer Science (MFCS-2016).
Cite as
Virginia Vassilevska Williams. RNA-Folding - From Hardness to Algorithms (Invited Talk). In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, p. 5:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{vassilevskawilliams:LIPIcs.MFCS.2016.5,
author = {Vassilevska Williams, Virginia},
title = {{RNA-Folding - From Hardness to Algorithms}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {5:1--5:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.5},
URN = {urn:nbn:de:0030-drops-65115},
doi = {10.4230/LIPIcs.MFCS.2016.5},
annote = {Keywords: RNA folding, matrix multiplication}
}
Document
Integer Factoring Using Small Algebraic Dependencies
Abstract
Integer factoring is a curious number theory problem with wide applications in complexity and cryptography. The best known algorithm to factor a number n takes time, roughly, exp(2*log^{1/3}(n)*log^{2/3}(log(n))) (number field sieve, 1989). One basic idea used is to find two squares, possibly in a number field, that are congruent modulo n. Several variants of this idea have been utilized to get other factoring algorithms in the last century. In this work we intend to explore new ideas towards integer factoring. In particular, we adapt the AKS primality test (2004) ideas for integer factoring.
In the motivating case of semiprimes n=pq, i.e. p<q are primes, we exploit the difference in the two Frobenius morphisms (one over F_p and the other over F_q) to factor n in special cases. Specifically, our algorithm is polynomial time (on number theoretic conjectures) if we know a small algebraic dependence between p,q. We discuss families of n where our algorithm is significantly faster than the algorithms based on known techniques.
Cite as
Manindra Agrawal, Nitin Saxena, and Shubham Sahai Srivastava. Integer Factoring Using Small Algebraic Dependencies. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{agrawal_et_al:LIPIcs.MFCS.2016.6,
author = {Agrawal, Manindra and Saxena, Nitin and Srivastava, Shubham Sahai},
title = {{Integer Factoring Using Small Algebraic Dependencies}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {6:1--6:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.6},
URN = {urn:nbn:de:0030-drops-64234},
doi = {10.4230/LIPIcs.MFCS.2016.6},
annote = {Keywords: integer, factorization, factoring integers, algebraic dependence, dependencies}
}
Document
Routing with Congestion in Acyclic Digraphs
Abstract
We study the version of the k-disjoint paths problem where k demand pairs (s_1,t_1), ..., (s_k,t_k) are specified in the input and the paths in the solution are allowed to intersect, but such that no vertex is on more than c paths. We show that on directed acyclic graphs the problem is solvable in time n^{O(d)} if we allow congestion k-d for k paths. Furthermore, we show that, under a suitable complexity theoretic assumption, the problem cannot be solved in time f(k)n^{o(d*log(d))} for any computable function f.
Cite as
Saeed Akhoondian Amiri, Stephan Kreutzer, Dániel Marx, and Roman Rabinovich. Routing with Congestion in Acyclic Digraphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 7:1-7:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{amiri_et_al:LIPIcs.MFCS.2016.7,
author = {Amiri, Saeed Akhoondian and Kreutzer, Stephan and Marx, D\'{a}niel and Rabinovich, Roman},
title = {{Routing with Congestion in Acyclic Digraphs}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {7:1--7:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.7},
URN = {urn:nbn:de:0030-drops-64244},
doi = {10.4230/LIPIcs.MFCS.2016.7},
annote = {Keywords: algorithms, disjoint paths, congestion, acyclic digraphs, XP, W\lbrack1\rbrack-hard}
}
Document
Stochastic Timed Games Revisited
Abstract
Stochastic timed games (STGs), introduced by Bouyer and Forejt, naturally generalize both continuous-time Markov chains and timed automata by providing a partition of the locations between those controlled by two players (Player Box and Player Diamond) with competing objectives and those governed by stochastic laws. Depending on the number of players - 2, 1, or 0 - subclasses of stochastic timed games are often classified as 2 1/2-player, 1 1/2-player, and 1/2-player games where the 1/2 symbolizes the presence of the stochastic "nature" player. For STGs with reachability objectives it is known that 1 1/2-player one-clock STGs are decidable for qualitative objectives, and that 2 1/2-player three-clock STGs are undecidable for quantitative reachability objectives. This paper further refines the gap in this decidability spectrum. We show that quantitative reachability objectives are already undecidable for 1 1/2 player four-clock STGs, and even under the time-bounded restriction for 2 1/2-player five-clock STGs. We also obtain a class of 1 1/2, 2 1/2 player STGs for which the quantitative reachability problem is decidable.
Cite as
S. Akshay, Patricia Bouyer, Shankara Narayanan Krishna, Lakshmi Manasa, and Ashutosh Trivedi. Stochastic Timed Games Revisited. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{akshay_et_al:LIPIcs.MFCS.2016.8,
author = {Akshay, S. and Bouyer, Patricia and Krishna, Shankara Narayanan and Manasa, Lakshmi and Trivedi, Ashutosh},
title = {{Stochastic Timed Games Revisited}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {8:1--8:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.8},
URN = {urn:nbn:de:0030-drops-64985},
doi = {10.4230/LIPIcs.MFCS.2016.8},
annote = {Keywords: timed automata, stochastic games, two-counter machines}
}
Document
Inequity Aversion Pricing over Social Networks: Approximation Algorithms and Hardness Results
Abstract
We study a revenue maximization problem in the context of social networks. Namely, we consider a model introduced by Alon, Mansour, and Tennenholtz (EC 2013) that captures inequity aversion, i.e., prices offered to neighboring vertices should not be significantly different. We first provide approximation algorithms for a natural class of instances, referred to as the class of single-value revenue functions. Our results improve on the current state of the art, especially when the number of distinct prices is small. This applies, for example, to settings where the seller will only consider a fixed number of discount types or special offers. We then resolve one of the open questions posed in Alon et al., by establishing APX-hardness for the problem. Surprisingly, we further show that the problem is NP-complete even when the price differences are allowed to be relatively large. Finally, we also provide some extensions of the model of Alon et al., regarding the allowed set of prices.
Cite as
Georgios Amanatidis, Evangelos Markakis, and Krzysztof Sornat. Inequity Aversion Pricing over Social Networks: Approximation Algorithms and Hardness Results. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 9:1-9:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{amanatidis_et_al:LIPIcs.MFCS.2016.9,
author = {Amanatidis, Georgios and Markakis, Evangelos and Sornat, Krzysztof},
title = {{Inequity Aversion Pricing over Social Networks: Approximation Algorithms and Hardness Results}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {9:1--9:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.9},
URN = {urn:nbn:de:0030-drops-64254},
doi = {10.4230/LIPIcs.MFCS.2016.9},
annote = {Keywords: inequity aversion, social networks, revenue maximization}
}
Document
Trading Determinism for Time in Space Bounded Computations
Abstract
Savitch showed in 1970 that nondeterministic logspace (NL) is contained in deterministic O(log^2(n)) space but his algorithm requires quasipolynomial time. The question whether we can have a deterministic algorithm for every problem in NL that requires polylogarithmic space and simultaneously runs in polynomial time was left open.
In this paper we give a partial solution to this problem and show that for every language in NL there exists an unambiguous nondeterministic algorithm that requires O(log^2(n)) space and simultaneously runs in polynomial time.
Cite as
Vivek Anand T Kallampally and Raghunath Tewari. Trading Determinism for Time in Space Bounded Computations. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{kallampally_et_al:LIPIcs.MFCS.2016.10,
author = {Kallampally, Vivek Anand T and Tewari, Raghunath},
title = {{Trading Determinism for Time in Space Bounded Computations}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {10:1--10:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.10},
URN = {urn:nbn:de:0030-drops-64268},
doi = {10.4230/LIPIcs.MFCS.2016.10},
annote = {Keywords: space complexity, unambiguous computations, Savitch's Theorem}
}
Document
Families of DFAs as Acceptors of omega-Regular Languages
Abstract
Families of DFAs (FDFAs) provide an alternative formalism for recognizing omega-regular languages. The motivation for introducing them was a desired correlation between the automaton states and right congruence relations, in a manner similar to the Myhill-Nerode theorem for regular languages. This correlation is beneficial for learning algorithms, and indeed it was recently shown that omega-regular languages can be learned from membership and equivalence queries, using FDFAs as the acceptors.
In this paper, we look into the question of how suitable FDFAs are for defining omega-regular languages. Specifically, we look into the complexity of performing Boolean operations, such as complementation and intersection, on FDFAs, the complexity of solving decision problems, such as emptiness and language containment, and the succinctness of FDFAs compared to standard deterministic and nondeterministic omega-automata.
We show that FDFAs enjoy the benefits of deterministic automata with respect to Boolean operations and decision problems. Namely, they can all be performed in nondeterministic logarithmic space.
We provide polynomial translations of deterministic Buchi and coBuchi automata to FDFAs and of FDFAs to nondeterministic Buchi automata (NBAs). We show that translation of an NBA to an FDFA may involve an exponential blowup. Last, we show that FDFAs are more succinct than deterministic parity automata (DPAs) in the sense that translating a DPA to an FDFA can always be done with only a polynomial increase, yet the other direction involves an inevitable exponential blowup in the worst case.
Cite as
Dana Angluin, Udi Boker, and Dana Fisman. Families of DFAs as Acceptors of omega-Regular Languages. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{angluin_et_al:LIPIcs.MFCS.2016.11,
author = {Angluin, Dana and Boker, Udi and Fisman, Dana},
title = {{Families of DFAs as Acceptors of omega-Regular Languages}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {11:1--11:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.11},
URN = {urn:nbn:de:0030-drops-64274},
doi = {10.4230/LIPIcs.MFCS.2016.11},
annote = {Keywords: finite automata, omega regular languages}
}
Document
On the Complexity of Probabilistic Trials for Hidden Satisfiability Problems
Abstract
What is the minimum amount of information and time needed to solve 2SAT? When the instance is known, it can be solved in polynomial time, but is this also possible without knowing the instance? Bei, Chen and Zhang (STOC'13) considered a model where the input is accessed by proposing possible assignments to a special oracle. This oracle, on encountering some constraint unsatisfied by the proposal, returns only the constraint index. It turns out that, in this model, even 1SAT cannot be solved in polynomial time unless P=NP. Hence, we consider a model in which the input is accessed by proposing probability distributions over assignments to the variables. The oracle then returns the index of the constraint that is most likely to be violated by this distribution. We show that the information obtained this way is sufficient to solve 1SAT in polynomial time, even when the clauses can be repeated. For 2SAT, as long as there are no repeated clauses, in polynomial time we can even learn an equivalent formula for the hidden instance and hence also solve it. Furthermore, we extend these results to the quantum regime. We show that in this setting 1QSAT can be solved in polynomial time up to constant precision, and 2QSAT can be learnt in polynomial time up to inverse polynomial precision.
Cite as
Itai Arad, Adam Bouland, Daniel Grier, Miklos Santha, Aarthi Sundaram, and Shengyu Zhang. On the Complexity of Probabilistic Trials for Hidden Satisfiability Problems. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{arad_et_al:LIPIcs.MFCS.2016.12,
author = {Arad, Itai and Bouland, Adam and Grier, Daniel and Santha, Miklos and Sundaram, Aarthi and Zhang, Shengyu},
title = {{On the Complexity of Probabilistic Trials for Hidden Satisfiability Problems}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {12:1--12:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.12},
URN = {urn:nbn:de:0030-drops-64284},
doi = {10.4230/LIPIcs.MFCS.2016.12},
annote = {Keywords: computational complexity, satisfiability problems, trial and error, quantum computing, learning theory}
}
Document
The Parameterized Complexity of Fixing Number and Vertex Individualization in Graphs
Abstract
In this paper we study the complexity of the following problems:
1. Given a colored graph X=(V,E,c), compute a minimum cardinality set of vertices S (subset of V) such that no nontrivial automorphism of X fixes all vertices in S. A closely related problem is computing a minimum base S for a permutation group G <= S_n given by generators, i.e., a minimum cardinality subset S of [n] such that no nontrivial permutation in G fixes all elements of S. Our focus is mainly on the parameterized complexity of these problems. We show that when k=|S| is treated as parameter, then both problems are MINI[1]-hard. For the dual problems, where k=n-|S| is the parameter, we give FPT~algorithms.
2. A notion closely related to fixing is called individualization. Individualization combined with the Weisfeiler-Leman procedure is a fundamental technique in algorithms for Graph Isomorphism. Motivated by the power of individualization, in the present paper we explore the complexity of individualization: what is the minimum number of vertices we need to individualize in a given graph such that color refinement "succeeds" on it. Here "succeeds" could have different interpretations, and we consider the following: It could mean the individualized graph becomes: (a) discrete, (b) amenable, (c)compact, or (d) refinable. In particular, we study the parameterized versions of these problems where the parameter is the number of vertices individualized. We show a dichotomy: For graphs with color classes of size at most 3 these problems can be solved in polynomial time, while starting from color class size 4 they become W[P]-hard.
Cite as
Vikraman Arvind, Frank Fuhlbrück, Johannes Köbler, Sebastian Kuhnert, and Gaurav Rattan. The Parameterized Complexity of Fixing Number and Vertex Individualization in Graphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{arvind_et_al:LIPIcs.MFCS.2016.13,
author = {Arvind, Vikraman and Fuhlbr\"{u}ck, Frank and K\"{o}bler, Johannes and Kuhnert, Sebastian and Rattan, Gaurav},
title = {{The Parameterized Complexity of Fixing Number and Vertex Individualization in Graphs}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {13:1--13:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.13},
URN = {urn:nbn:de:0030-drops-64294},
doi = {10.4230/LIPIcs.MFCS.2016.13},
annote = {Keywords: parameterized complexity, graph automorphism, fixing number, base size, individualization}
}
Document
Real Interactive Proofs for VPSPACE
Abstract
We study interactive proofs in the framework of real number complexity as introduced by Blum, Shub, and Smale. The ultimate goal is to give a Shamir like characterization of the real counterpart IP_R of classical IP. Whereas classically Shamir's result implies IP = PSPACE = PAT = PAR, in our framework a major difficulty arises from the fact that in contrast to Turing complexity theory the real number classes PAR_R and PAT_R differ and space resources considered alone are not meaningful. It is not obvious to see whether IP_R is characterized by one of them - and if so by which.
In recent work the present authors established an upper bound IP_R is a subset of MA(Exists)R, where MA(Exists)R is a complexity class satisfying PAR_R is a strict subset of MA(Exists)R, which is a subset of PAT_R and conjectured to be different from PAT_R. The goal of the present paper is to complement this result and to prove interesting lower bounds for IP_R. More precisely, we design interactive real protocols for a large class of functions introduced by Koiran and Perifel and denoted by UniformVSPACE^0. As consequence, we show PAR_R is a subset of IP_R, which in particular implies co-NP_R is a subset of IP_R, and P_R^{Res} is a subset of IP_R, where Res denotes certain multivariate Resultant polynomials.
Our proof techniques are guided by the question in how far Shamir's classical proof can be used as well in the real number setting. Towards this aim results by Koiran and Perifel on UniformVSPACE^0 are extremely helpful.
Cite as
Martijn Baartse and Klaus Meer. Real Interactive Proofs for VPSPACE. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 14:1-14:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{baartse_et_al:LIPIcs.MFCS.2016.14,
author = {Baartse, Martijn and Meer, Klaus},
title = {{Real Interactive Proofs for VPSPACE}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {14:1--14:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.14},
URN = {urn:nbn:de:0030-drops-64300},
doi = {10.4230/LIPIcs.MFCS.2016.14},
annote = {Keywords: interactive proofs, real number computation, Shamir's theorem}
}
Document
Synchronizing Data Words for Register Automata
Abstract
Register automata (RAs) are finite automata extended with a finite set of registers to store and compare data. We study the concept of synchronizing data words in RAs: Does there exist a data word that sends all states of the RA to a single state?
For deterministic RAs with k registers (k-DRAs), we prove that inputting data words with 2k+1 distinct data, from the infinite data domain, is sufficient to synchronize. We show that the synchronizing problem for DRAs is in general PSPACE-complete, and is NLOGSPACE-complete for 1-DRAs. For nondeterministic RAs (NRAs), we show that Ackermann(n) distinct data (where n is the size of RA) might be necessary to synchronize. The synchronizing problem for NRAs is in general undecidable, however, we establish Ackermann-completeness of the problem for 1-NRAs. Our most substantial achievement is proving NEXPTIME-completeness of the length-bounded synchronizing problem in NRAs (length encoded in binary). A variant of this last construction allows to prove that the bounded universality problem in NRAs is co-NEXPTIME-complete.
Cite as
Parvaneh Babari, Karin Quaas, and Mahsa Shirmohammadi. Synchronizing Data Words for Register Automata. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{babari_et_al:LIPIcs.MFCS.2016.15,
author = {Babari, Parvaneh and Quaas, Karin and Shirmohammadi, Mahsa},
title = {{Synchronizing Data Words for Register Automata}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {15:1--15:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.15},
URN = {urn:nbn:de:0030-drops-64996},
doi = {10.4230/LIPIcs.MFCS.2016.15},
annote = {Keywords: data words, register automata, synchronizing problem, Ackermann-completeness, bounded universality, regular-like expressions with squaring}
}
Document
On the Sensitivity Conjecture for Read-k Formulas
Abstract
Various combinatorial/algebraic parameters are used to quantify the complexity of a Boolean function. Among them, sensitivity is one of the simplest and block sensitivity is one of the most useful. Nisan (1989) and Nisan and Szegedy (1991) showed that block sensitivity and several other parameters, such as certificate complexity, decision tree depth, and degree over R, are all polynomially related to one another. The sensitivity conjecture states that there is also a polynomial relationship between sensitivity and block sensitivity, thus supplying the "missing link".
Since its introduction in 1991, the sensitivity conjecture has remained a challenging open question in the study of Boolean functions. One natural approach is to prove it for special classes of functions. For instance, the conjecture is known to be true for monotone functions, symmetric functions, and
functions describing graph properties.
In this paper, we consider the conjecture for Boolean functions computable by read-k formulas. A read-k formula is a tree in which each variable appears at most k times among the leaves and has Boolean gates at its internal nodes. We show that the sensitivity conjecture holds for read-once formulas with gates computing symmetric functions. We next consider regular formulas with OR and AND gates. A formula is regular if it is a leveled tree with all gates at a given level having the same fan-in and computing the same function. We prove the sensitivity conjecture for constant depth regular read-k formulas for constant k.
Cite as
Mitali Bafna, Satyanarayana V. Lokam, Sébastien Tavenas, and Ameya Velingker. On the Sensitivity Conjecture for Read-k Formulas. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{bafna_et_al:LIPIcs.MFCS.2016.16,
author = {Bafna, Mitali and Lokam, Satyanarayana V. and Tavenas, S\'{e}bastien and Velingker, Ameya},
title = {{On the Sensitivity Conjecture for Read-k Formulas}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {16:1--16:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.16},
URN = {urn:nbn:de:0030-drops-64317},
doi = {10.4230/LIPIcs.MFCS.2016.16},
annote = {Keywords: sensitivity conjecture, read-k formulas, analysis of Boolean functions}
}
Document
Graph Properties in Node-Query Setting: Effect of Breaking Symmetry
Abstract
The query complexity of graph properties is well-studied when queries are on the edges. We investigate the same when queries are on the nodes. In this setting a graph G = (V,E) on n vertices and a property P are given. A black-box access to an unknown subset S of V is provided via queries of the form "Does i belong to S?". We are interested in the minimum number of queries needed in the worst case in order to determine whether G[S] - the subgraph of G induced on S - satisfies P.
Our primary motivation to study this model comes from the fact that it allows us to initiate a systematic study of breaking symmetry in the context of query complexity of graph properties. In particular, we focus on the hereditary graph properties - properties that are closed under deletion of vertices as well as edges. The famous Evasiveness Conjecture asserts that even with a minimal symmetry assumption on G, namely that of vertex-transitivity, the query complexity for any hereditary graph property in our setting is the worst possible, i.e., n.
We show that in the absence of any symmetry on G it can fall as low as O(n^{1/(d + 1)}) where d denotes the minimum possible degree of a minimal forbidden sub-graph for P. In particular, every hereditary property benefits at least quadratically. The main question left open is: Can it go exponentially low for some hereditary property? We show that the answer is no for any hereditary property with finitely many forbidden subgraphs by exhibiting a bound of Omega(n^{1/k}) for a constant k depending only on the property. For general ones we rule out the possibility of the query complexity falling down to constant by showing Omega(log(n)*log(log(n))) bound. Interestingly, our lower bound proofs rely on the famous Sunflower Lemma due to Erdos and Rado.
Cite as
Nikhil Balaji, Samir Datta, Raghav Kulkarni, and Supartha Podder. Graph Properties in Node-Query Setting: Effect of Breaking Symmetry. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{balaji_et_al:LIPIcs.MFCS.2016.17,
author = {Balaji, Nikhil and Datta, Samir and Kulkarni, Raghav and Podder, Supartha},
title = {{Graph Properties in Node-Query Setting: Effect of Breaking Symmetry}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {17:1--17:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.17},
URN = {urn:nbn:de:0030-drops-64329},
doi = {10.4230/LIPIcs.MFCS.2016.17},
annote = {Keywords: query complexity, graph properties, symmetry and computation, forbidden subgraph}
}
Document
Stable States of Perturbed Markov Chains
Abstract
Given an infinitesimal perturbation of a discrete-time finite Markov chain, we seek the states that are stable despite the perturbation, i.e. the states whose weights in the stationary distributions can be bounded away from 0 as the noise fades away. Chemists, economists, and computer scientists have been studying irreducible perturbations built with monomial maps. Under these assumptions, Young proved the existence of and computed the stable states in cubic time. We fully drop these assumptions, generalize Young's technique, and show that stability is decidable as long as f in O(g) is. Furthermore, if the perturbation maps (and their multiplications) satisfy f in O(g) or g in O(f), we prove the existence of and compute the stable states and the metastable dynamics at all time scales where some states vanish. Conversely, if the big-O assumption does not hold, we build a perturbation with these maps and no stable state. Our algorithm also runs in cubic time despite the weak assumptions and the additional work. Proving its correctness relies on new or rephrased results in Markov chain theory, and on algebraic abstractions thereof.
Cite as
Volker Betz and Stéphane Le Roux. Stable States of Perturbed Markov Chains. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{betz_et_al:LIPIcs.MFCS.2016.18,
author = {Betz, Volker and Le Roux, St\'{e}phane},
title = {{Stable States of Perturbed Markov Chains}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {18:1--18:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.18},
URN = {urn:nbn:de:0030-drops-64335},
doi = {10.4230/LIPIcs.MFCS.2016.18},
annote = {Keywords: evolution, metastability, tropical, shortest path, SCC, cubic time}
}
Document
On Degeneration of Tensors and Algebras
Abstract
An important building block in all current asymptotically fast algorithms for matrix multiplication are tensors with low border rank, that is, tensors whose border rank is equal or very close to their size. To find new asymptotically fast algorithms for matrix multiplication, it seems to be important to understand those tensors whose border rank is as small as possible, so called tensors of minimal border rank.
We investigate the connection between degenerations of associative algebras and degenerations of their structure tensors in the sense of Strassen. It allows us to describe an open subset of n*n*n tensors of minimal border rank in terms of smoothability of commutative algebras. We describe the smoothable algebra associated to the Coppersmith-Winograd tensor and prove a lower bound for the border rank of the tensor used in the "easy construction" of Coppersmith and Winograd.
Cite as
Markus Bläser and Vladimir Lysikov. On Degeneration of Tensors and Algebras. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 19:1-19:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{blaser_et_al:LIPIcs.MFCS.2016.19,
author = {Bl\"{a}ser, Markus and Lysikov, Vladimir},
title = {{On Degeneration of Tensors and Algebras}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {19:1--19:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.19},
URN = {urn:nbn:de:0030-drops-64343},
doi = {10.4230/LIPIcs.MFCS.2016.19},
annote = {Keywords: bilinear complexity, border rank, commutative algebras, lower bounds}
}
Document
Using Contracted Solution Graphs for Solving Reconfiguration Problems
Abstract
We introduce a dynamic programming method for solving reconfiguration problems, based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions that decrease the graph size without losing any critical information needed to solve the reconfiguration problem under consideration. As an example, we consider a well-studied problem: given two k-colorings alpha and beta of a graph G, can alpha be modified into beta by recoloring one vertex of G at a time, while maintaining a k-coloring throughout? By applying our method in combination with a thorough exploitation of the graph structure we obtain a polynomial-time algorithm for (k-2)-connected chordal graphs.
Cite as
Paul Bonsma and Daniël Paulusma. Using Contracted Solution Graphs for Solving Reconfiguration Problems. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{bonsma_et_al:LIPIcs.MFCS.2016.20,
author = {Bonsma, Paul and Paulusma, Dani\"{e}l},
title = {{Using Contracted Solution Graphs for Solving Reconfiguration Problems}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {20:1--20:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.20},
URN = {urn:nbn:de:0030-drops-64351},
doi = {10.4230/LIPIcs.MFCS.2016.20},
annote = {Keywords: reconfiguration, contraction, dynamic programming, graph coloring}
}
Document
Pointer Quantum PCPs and Multi-Prover Games
Abstract
The quantum PCP (QPCP) conjecture states that all problems in QMA, the quantum analogue of NP, admit quantum verifiers that only act on a constant number of qubits of a polynomial size quantum proof and have a constant gap between completeness and soundness. Despite an impressive body of work trying to prove or disprove the quantum PCP conjecture, it still remains widely open. The above-mentioned proof verification statement has also been shown equivalent to the QMA-completeness of the Local Hamiltonian problem with constant relative gap. Nevertheless, unlike in the classical case, no equivalent formulation in the language of multi-prover games is known.
In this work, we propose a new type of quantum proof systems, the Pointer QPCP, where a verifier first accesses a classical proof that he can use as a pointer to which qubits from the quantum part of the proof to access. We define the Pointer QPCP conjecture, that states that all problems in QMA admit quantum verifiers that first access a logarithmic number of bits from the classical part of a polynomial size proof, then act on a constant number of qubits from the quantum part of the proof, and have a constant gap between completeness and soundness. We define a new QMA-complete problem, the Set Local Hamiltonian problem, and a new restricted class of quantum multi-prover games, called CRESP games. We use them to provide two other equivalent statements to the Pointer QPCP conjecture: the Set Local Hamiltonian problem with constant relative gap is QMA-complete; and the approximation of the maximum acceptance probability of CRESP games up to a constant additive factor is as hard as QMA. Our new conjecture is weaker than the original QPCP conjecture and hence provides a natural intermediate step towards proving the quantum PCP theorem. Furthermore, this is the first equivalence between a quantum PCP statement and the inapproximability of quantum multi-prover games.
Cite as
Alex B. Grilo, Iordanis Kerenidis, and Attila Pereszlényi. Pointer Quantum PCPs and Multi-Prover Games. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{grilo_et_al:LIPIcs.MFCS.2016.21,
author = {Grilo, Alex B. and Kerenidis, Iordanis and Pereszl\'{e}nyi, Attila},
title = {{Pointer Quantum PCPs and Multi-Prover Games}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {21:1--21:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.21},
URN = {urn:nbn:de:0030-drops-64364},
doi = {10.4230/LIPIcs.MFCS.2016.21},
annote = {Keywords: computational complexity, quantum computation, PCP theorem}
}
Document
A Formal Exploration of Nominal Kleene Algebra
Abstract
An axiomatisation of Nominal Kleene Algebra has been proposed by Gabbay and Ciancia, and then shown to be complete and decidable by Kozen et al. However, one can think of at least four different formulations for a Kleene Algebra with names: using freshness conditions or a presheaf structure (types), and with explicit permutations or not. We formally show that these variations are all equivalent.
Then we introduce an extension of Nominal Kleene Algebra, motivated by relational models of programming languages. The idea is to let letters (i.e., atomic programs) carry a set of names, rather than being reduced to a single name. We formally show that this extension is at least as expressive as the original one, and that it may be presented with or without a presheaf structure, and with or without syntactic permutations. Whether this extension is strictly more
expressive remains open.
All our results were formally checked using the Coq proof assistant.
Cite as
Paul Brunet and Damien Pous. A Formal Exploration of Nominal Kleene Algebra. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 22:1-22:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{brunet_et_al:LIPIcs.MFCS.2016.22,
author = {Brunet, Paul and Pous, Damien},
title = {{A Formal Exploration of Nominal Kleene Algebra}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {22:1--22:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.22},
URN = {urn:nbn:de:0030-drops-64379},
doi = {10.4230/LIPIcs.MFCS.2016.22},
annote = {Keywords: Nominal sets, Kleene algebra, equational theory, Coq}
}
Document
On the Implicit Graph Conjecture
Abstract
The implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined in terms of complexity classes such as P and EXP. For instance, GP denotes the class of graph classes that have a labeling scheme with a polynomial-time computable label decoder. Until now it was not even known whether GP is a strict subset of GR where R is the class of recursive languages. We show that this is indeed the case and reveal a strict hierarchy akin to classical complexity. We also show that classes such as GP can be characterized in terms of graph parameters. This could mean that certain algorithmic problems are feasible on every graph class in GP. Lastly, we define a more restrictive class of label decoders using first-order logic that already contains many natural graph classes such as forests and interval graphs. We give an alternative characterization of this class in terms of directed acyclic graphs. By showing that some small, hereditary graph class cannot be expressed with such label decoders a weaker form of the implicit graph conjecture could be disproven.
Cite as
Maurice Chandoo. On the Implicit Graph Conjecture. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 23:1-23:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{chandoo:LIPIcs.MFCS.2016.23,
author = {Chandoo, Maurice},
title = {{On the Implicit Graph Conjecture}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {23:1--23:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.23},
URN = {urn:nbn:de:0030-drops-64389},
doi = {10.4230/LIPIcs.MFCS.2016.23},
annote = {Keywords: adjacency labeling scheme, complexity classes, diagonalization, logic}
}
Document
Nested Weighted Limit-Average Automata of Bounded Width
Abstract
While weighted automata provide a natural framework to express quantitative properties, many basic properties like average response time cannot be expressed with weighted automata. Nested weighted automata extend weighted automata and consist of a master automaton and a set of slave automata that are invoked by the master automaton. Nested weighted automata are strictly more expressive than weighted automata (e.g., average response time can be expressed with nested weighted automata), but the basic decision questions have higher complexity (e.g., for deterministic automata, the emptiness question for nested weighted automata is PSPACE-hard, whereas the corresponding complexity for weighted automata is PTIME). We consider a natural subclass of nested weighted automata where at any point at most a bounded number k of slave automata can be active. We focus on automata whose master value function is the limit average. We show that these nested weighted automata with bounded width are strictly more expressive than weighted automata (e.g., average response time with no overlapping requests can be expressed with bound k=1, but not with non-nested weighted automata). We show that the complexity of the basic decision problems (i.e., emptiness and universality) for the subclass with k constant matches the complexity for weighted automata. Moreover, when k is part of the input given in unary we establish PSPACE-completeness.
Cite as
Krishnendu Chatterjee, Thomas A. Henzinger, and Jan Otop. Nested Weighted Limit-Average Automata of Bounded Width. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{chatterjee_et_al:LIPIcs.MFCS.2016.24,
author = {Chatterjee, Krishnendu and Henzinger, Thomas A. and Otop, Jan},
title = {{Nested Weighted Limit-Average Automata of Bounded Width}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {24:1--24:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.24},
URN = {urn:nbn:de:0030-drops-64397},
doi = {10.4230/LIPIcs.MFCS.2016.24},
annote = {Keywords: weighted automata, nested weighted automata, complexity, mean-payoff}
}
Document
Conditionally Optimal Algorithms for Generalized Büchi Games
Abstract
Games on graphs provide the appropriate framework to study several central problems in computer science, such as verification and synthesis of reactive systems. One of the most basic objectives for games on graphs is the liveness (or Büchi) objective that given a target set of vertices requires that some vertex in the target set is visited infinitely often. We study generalized Büchi objectives (i.e., conjunction of liveness objectives), and implications between two generalized Büchi objectives (known as GR(1) objectives), that arise in numerous applications in computer-aided verification. We present improved algorithms and conditional super-linear lower bounds based on widely believed assumptions about the complexity of (A1) combinatorial Boolean matrix multiplication and (A2) CNF-SAT. We consider graph games with n vertices, m edges, and generalized Büchi objectives with k conjunctions. First, we present an algorithm with running time O(k*n^2), improving the previously known O(k*n*m) and O(k^2*n^2) worst-case bounds. Our algorithm is optimal for dense graphs under (A1). Second, we show that the basic algorithm for the problem is optimal for sparse graphs when the target sets have constant size under (A2). Finally, we consider GR(1) objectives, with k_1 conjunctions in the antecedent and k_2 conjunctions in the consequent, and present an O(k_1 k_2 n^{2.5})-time algorithm, improving the previously known O(k_1*k_2*n*m)-time algorithm for m > n^{1.5}.
Cite as
Krishnendu Chatterjee, Wolfgang Dvorák, Monika Henzinger, and Veronika Loitzenbauer. Conditionally Optimal Algorithms for Generalized Büchi Games. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{chatterjee_et_al:LIPIcs.MFCS.2016.25,
author = {Chatterjee, Krishnendu and Dvor\'{a}k, Wolfgang and Henzinger, Monika and Loitzenbauer, Veronika},
title = {{Conditionally Optimal Algorithms for Generalized B\"{u}chi Games}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {25:1--25:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.25},
URN = {urn:nbn:de:0030-drops-64403},
doi = {10.4230/LIPIcs.MFCS.2016.25},
annote = {Keywords: generalized B\"{u}chi objective, GR(1) objective, conditional lower bounds, graph games, graph algorithms, computer-aided verification}
}
Document
FPT Algorithms for Plane Completion Problems
Abstract
The Plane Subgraph (resp. Topological Minor) Completion problem asks, given a (possibly disconnected) plane (multi)graph Gamma and a connected plane (multi)graph Delta, whether it is possible to add edges in Gamma without violating the planarity of its embedding so that it contains some subgraph (resp. topological minor) that is topologically isomorphic to Delta. We give FPT algorithms that solve both problems in f(|E(Delta)|)*|E(\Gamma)|^{2} steps. Moreover, for the Plane Subgraph Completion problem we show that f(k)=2^{O(k*log(k))}.
Cite as
Dimitris Chatzidimitriou, Archontia C. Giannopoulou, Spyridon Maniatis, Clément Requilé, Dimitrios M. Thilikos, and Dimitris Zoros. FPT Algorithms for Plane Completion Problems. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{chatzidimitriou_et_al:LIPIcs.MFCS.2016.26,
author = {Chatzidimitriou, Dimitris and Giannopoulou, Archontia C. and Maniatis, Spyridon and Requil\'{e}, Cl\'{e}ment and Thilikos, Dimitrios M. and Zoros, Dimitris},
title = {{FPT Algorithms for Plane Completion Problems}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {26:1--26:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.26},
URN = {urn:nbn:de:0030-drops-64418},
doi = {10.4230/LIPIcs.MFCS.2016.26},
annote = {Keywords: completion problems, FPT, plane graphs, topological isomorphism}
}
Document
Some Lower Bounds in Parameterized AC^0
Abstract
We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical AC^0. Among others, we derive such a lower bound for all fpt-approximations of the parameterized clique problem and for a parameterized halting problem, which recently turned out to link problems of computational complexity, descriptive complexity, and proof theory. To show the first lower bound, we prove a strong AC^0 version of the planted clique conjecture: AC^0-circuits asymptotically almost surely can not distinguish between a random graph and this graph with a randomly planted clique of any size <= n^xi (where 0 <= xi < 1).
Cite as
Yijia Chen and Jörg Flum. Some Lower Bounds in Parameterized AC^0. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{chen_et_al:LIPIcs.MFCS.2016.27,
author = {Chen, Yijia and Flum, J\"{o}rg},
title = {{Some Lower Bounds in Parameterized AC^0}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {27:1--27:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.27},
URN = {urn:nbn:de:0030-drops-64423},
doi = {10.4230/LIPIcs.MFCS.2016.27},
annote = {Keywords: parameterized AC^0, lower bound, clique, halting problem}
}
Document
Space-Efficient Approximation Scheme for Maximum Matching in Sparse Graphs
Abstract
We present a Logspace Approximation Scheme (LSAS), i.e. an approximation algorithm for maximum matching in planar graphs (not necessarily bipartite) that achieves an approximation ratio arbitrarily close to one, using only logarithmic space. This deviates from the well known Baker's approach for approximation in planar graphs by avoiding the use of distance computation - which is not known to be in Logspace. Our algorithm actually works for any "recursively sparse" graph class which contains a linear size matching and also for certain other classes like bounded genus graphs.
The scheme is based on an LSAS in bounded degree graphs which are not known to be amenable to Baker's method. We solve the bounded degree case by parallel augmentation of short augmenting paths. Finding a large number of such disjoint paths can, in turn, be reduced to finding a large independent set in a bounded degree graph. The bounded degree assumption allows us to obtain a Logspace algorithm.
Cite as
Samir Datta, Raghav Kulkarni, and Anish Mukherjee. Space-Efficient Approximation Scheme for Maximum Matching in Sparse Graphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 28:1-28:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{datta_et_al:LIPIcs.MFCS.2016.28,
author = {Datta, Samir and Kulkarni, Raghav and Mukherjee, Anish},
title = {{Space-Efficient Approximation Scheme for Maximum Matching in Sparse Graphs}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {28:1--28:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.28},
URN = {urn:nbn:de:0030-drops-64436},
doi = {10.4230/LIPIcs.MFCS.2016.28},
annote = {Keywords: maximum matching, approximation scheme, logspace, planar graphs}
}
Document
Logical Characterization of Bisimulation for Transition Relations over Probability Distributions with Internal Actions
Abstract
In recent years the study of probabilistic transition systems has shifted to transition relations over distributions to allow for a smooth adaptation of the standard non-probabilistic apparatus. In this paper we study transition relations over probability distributions in a setting with internal actions. We provide new logics that characterize probabilistic strong, weak and branching bisimulation. Because these semantics may be considered too strong in the probabilistic context, Eisentraut et al. recently proposed weak distribution bisimulation. To show the flexibility of our approach based on the framework of van Glabbeek for the non-deterministic setting, we provide a novel logical characterization for the latter probabilistic equivalence as well.
Cite as
Matias David Lee and Erik P. de Vink. Logical Characterization of Bisimulation for Transition Relations over Probability Distributions with Internal Actions. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{lee_et_al:LIPIcs.MFCS.2016.29,
author = {Lee, Matias David and de Vink, Erik P.},
title = {{Logical Characterization of Bisimulation for Transition Relations over Probability Distributions with Internal Actions}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {29:1--29:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.29},
URN = {urn:nbn:de:0030-drops-64441},
doi = {10.4230/LIPIcs.MFCS.2016.29},
annote = {Keywords: probabilistic transition systems, weak bisimulations, logical characterization, transition relation over distributions, modal logics}
}
Document
Ackermannian Integer Compression and the Word Problem for Hydra Groups
Abstract
For a finitely presented group, the word problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is a complexity measure of a direct attack on the word problem by applying the defining relations. Dison and Riley showed that a "hydra phenomenon" gives rise to novel groups with extremely fast growing (Ackermannian) Dehn functions. Here we show that nevertheless, there are efficient (polynomial time) solutions to the word problems of these groups. Our main innovation is a means of computing efficiently with enormous integers which are represented in compressed forms by strings of Ackermann functions.
Cite as
Will Dison, Eduard Einstein, and Timothy R. Riley. Ackermannian Integer Compression and the Word Problem for Hydra Groups. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 30:1-30:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{dison_et_al:LIPIcs.MFCS.2016.30,
author = {Dison, Will and Einstein, Eduard and Riley, Timothy R.},
title = {{Ackermannian Integer Compression and the Word Problem for Hydra Groups}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {30:1--30:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.30},
URN = {urn:nbn:de:0030-drops-64458},
doi = {10.4230/LIPIcs.MFCS.2016.30},
annote = {Keywords: Ackermann functions, hydra, word problem}
}
Document
A Note on the Advice Complexity of Multipass Randomized Logspace
Abstract
Investigating the complexity of randomized space-bounded machines that are allowed to make multiple passes over the random tape has been of recent interest. In particular, it has been shown that derandomizing such probabilistic machines yields a weak but new derandomization of probabilistic time-bounded classes.
In this paper we further explore the complexity of such machines. In particular, as our main result we show that for any epsilon<1, every language that is accepted by an O(n^epsilon)-pass, randomized logspace machine can be simulated in deterministic logspace with linear amount of advice. This result extends an earlier result of Fortnow and Klivans who showed that RL is in deterministic logspace with linear advice.
Cite as
Peter Dixon, Debasis Mandal, A. Pavan, and N. V. Vinodchandran. A Note on the Advice Complexity of Multipass Randomized Logspace. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 31:1-31:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{dixon_et_al:LIPIcs.MFCS.2016.31,
author = {Dixon, Peter and Mandal, Debasis and Pavan, A. and Vinodchandran, N. V.},
title = {{A Note on the Advice Complexity of Multipass Randomized Logspace}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {31:1--31:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.31},
URN = {urn:nbn:de:0030-drops-65003},
doi = {10.4230/LIPIcs.MFCS.2016.31},
annote = {Keywords: space-bounded computations, randomized machines, advice}
}
Document
Complexity of Constraint Satisfaction Problems over Finite Subsets of Natural Numbers
Abstract
We study the computational complexity of constraint satisfaction problems that are based on integer expressions and algebraic circuits. On input of a finite set of variables and a finite set of constraints the question is whether the variables can be mapped onto finite subsets of N (resp., finite intervals over N) such that all constraints are satisfied. According to the operations allowed in the constraints, the complexity varies over a wide range of complexity classes such as L, P, NP, PSPACE, NEXP, and even Sigma_1, the class of c.e. languages.
Cite as
Titus Dose. Complexity of Constraint Satisfaction Problems over Finite Subsets of Natural Numbers. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{dose:LIPIcs.MFCS.2016.32,
author = {Dose, Titus},
title = {{Complexity of Constraint Satisfaction Problems over Finite Subsets of Natural Numbers}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {32:1--32:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.32},
URN = {urn:nbn:de:0030-drops-64461},
doi = {10.4230/LIPIcs.MFCS.2016.32},
annote = {Keywords: computational complexity, constraint satisfaction problems, integer expressions and circuits}
}
Document
Faster Algorithms for the Maximum Common Subtree Isomorphism Problem
Abstract
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is NP-hard in general graphs. Confining to trees renders polynomial time algorithms possible and is of fundamental importance for approaches on more general graph classes.Various variants of this problem in trees have been intensively studied. We consider the general case, where trees are neither rooted nor ordered and the isomorphism is maximum w.r.t. a weight function on the mapped vertices and edges. For trees of order n and maximum degree Delta our algorithm achieves a running time of O(n^2*Delta) by exploiting the structure of the matching instances arising as subproblems. Thus our algorithm outperforms the best previously known approaches. No faster algorithm is possible for trees of bounded degree and for trees of unbounded degree we show that a further reduction of the running time would directly improve the best known approach to the assignment problem. Combining a polynomial-delay algorithm for the enumeration of all maximum common subtree isomorphisms with central ideas of our new algorithm leads to an improvement of its running time from O(n^6+T*n^2) to O(n^3+T*n*Delta), where n is the order of the larger tree, T is the number of different solutions, and Delta is the minimum of the maximum degrees of the input trees. Our theoretical results are supplemented by an experimental evaluation on synthetic and real-world instances.
Cite as
Andre Droschinsky, Nils M. Kriege, and Petra Mutzel. Faster Algorithms for the Maximum Common Subtree Isomorphism Problem. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 33:1-33:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{droschinsky_et_al:LIPIcs.MFCS.2016.33,
author = {Droschinsky, Andre and Kriege, Nils M. and Mutzel, Petra},
title = {{Faster Algorithms for the Maximum Common Subtree Isomorphism Problem}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {33:1--33:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.33},
URN = {urn:nbn:de:0030-drops-64475},
doi = {10.4230/LIPIcs.MFCS.2016.33},
annote = {Keywords: MCS, maximum common subtree, enumeration algorithms, maximum weight bipartite matchings}
}
Document
A Single-Exponential Fixed-Parameter Algorithm for Distance-Hereditary Vertex Deletion
Abstract
Vertex deletion problems ask whether it is possible to delete at most k vertices from a graph so that the resulting graph belongs to a specified graph class. Over the past years, the parameterized complexity of vertex deletion to a plethora of graph classes has been systematically researched. Here we present the first single-exponential fixed-parameter algorithm for vertex deletion to distance-hereditary graphs, a well-studied graph class which is particularly important in the context of vertex deletion due to its connection to the graph parameter rank-width. We complement our result with matching asymptotic lower bounds based on the exponential time hypothesis.
Cite as
Eduard Eiben, Robert Ganian, and O-joung Kwon. A Single-Exponential Fixed-Parameter Algorithm for Distance-Hereditary Vertex Deletion. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 34:1-34:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{eiben_et_al:LIPIcs.MFCS.2016.34,
author = {Eiben, Eduard and Ganian, Robert and Kwon, O-joung},
title = {{A Single-Exponential Fixed-Parameter Algorithm for Distance-Hereditary Vertex Deletion}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {34:1--34:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.34},
URN = {urn:nbn:de:0030-drops-64483},
doi = {10.4230/LIPIcs.MFCS.2016.34},
annote = {Keywords: distance-hereditary graphs, fixed-parameter algorithms, rank-width}
}
Document
Preprocessing Under Uncertainty: Matroid Intersection
Abstract
We continue the study of preprocessing under uncertainty that was initiated independently by Assadi et al. (FSTTCS 2015) and Fafianie et al. (STACS 2016). Here, we are given an instance of a tractable problem with a large static/known part and a small part that is dynamic/uncertain, and ask if there is an efficient algorithm that computes an instance of size polynomial in the uncertain part of the input, from which we can extract an optimal solution to the original instance for all (usually exponentially many) instantiations of the uncertain part.
In the present work, we focus on the Matroid Intersection problem. Amongst others we present a positive preprocessing result for the important case of finding a largest common independent set in two linear matroids. Motivated by an application for intersecting two gammoids we also revisit Maximum Flow. There we tighten a lower bound of Assadi et al. and give an alternative positive result for the case of low uncertain capacity that yields a Maximum Flow instance as output rather than a matrix.
Cite as
Stefan Fafianie, Eva-Maria C. Hols, Stefan Kratsch, and Vuong Anh Quyen. Preprocessing Under Uncertainty: Matroid Intersection. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{fafianie_et_al:LIPIcs.MFCS.2016.35,
author = {Fafianie, Stefan and Hols, Eva-Maria C. and Kratsch, Stefan and Quyen, Vuong Anh},
title = {{Preprocessing Under Uncertainty: Matroid Intersection}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {35:1--35:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.35},
URN = {urn:nbn:de:0030-drops-64490},
doi = {10.4230/LIPIcs.MFCS.2016.35},
annote = {Keywords: preprocessing, uncertainty, maximum flow, matroid intersection}
}
Document
Ride Sharing with a Vehicle of Unlimited Capacity
Abstract
A ride sharing problem is considered where we are given a graph, whose edges are equipped with a travel cost, plus a set of objects, each associated with a transportation request given by a pair of origin and destination nodes. A vehicle travels through the graph, carrying each object from its origin to its destination without any bound on the number of objects that can be simultaneously transported. The vehicle starts and terminates its ride at given nodes, and the goal is to compute a minimum-cost ride satisfying all requests. This ride sharing problem is shown to be tractable on paths by designing a O(h*log(h)+n) algorithm, with h being the number of distinct requests and with n being the number of nodes in the path. The algorithm is then used as a subroutine to efficiently solve instances defined over cycles, hence covering all graphs with maximum degree 2. This traces the frontier of tractability, since NP-hard instances are exhibited over trees whose maximum degree is 3.
Cite as
Angelo Fanelli and Greco Gianluigi. Ride Sharing with a Vehicle of Unlimited Capacity. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{fanelli_et_al:LIPIcs.MFCS.2016.36,
author = {Fanelli, Angelo and Gianluigi, Greco},
title = {{Ride Sharing with a Vehicle of Unlimited Capacity}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {36:1--36:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.36},
URN = {urn:nbn:de:0030-drops-64506},
doi = {10.4230/LIPIcs.MFCS.2016.36},
annote = {Keywords: vehicle routing, ride sharing, pick up and delivery problem}
}
Document
On the General Chain Pair Simplification Problem
Abstract
The Chain Pair Simplification problem (CPS) was posed by Bereg et al. who were motivated by the problem of efficiently computing and visualizing the structural resemblance between a pair of protein backbones. In this problem, given two polygonal chains of lengths n and m, the goal is to simplify both of them simultaneously, so that the lengths of the resulting simplifications as well as the discrete Frechet distance between them are bounded. When the vertices of the simplifications are arbitrary (i.e., not necessarily from the original chains), the problem is called General CPS (GCPS).
In this paper we consider for the first time the complexity of GCPS under both the discrete Frechet distance (GCPS-3F) and the Hausdorff distance (GCPS-2H). (In the former version, the quality of the two simplifications is measured by the discrete Fr'echet distance, and in the latter version it is measured by the Hausdorff distance.) We prove that GCPS-3F is polynomially solvable, by presenting an widetilde-O((n+m)^6 min{n,m}) time algorithm for the corresponding minimization problem. We also present an O((n+m)^4) 2-approximation algorithm for the problem. On the other hand, we show that GCPS-2H is NP-complete, and present an approximation algorithm for the problem.
Cite as
Chenglin Fan, Omrit Filtser, Matthew J. Katz, and Binhai Zhu. On the General Chain Pair Simplification Problem. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 37:1-37:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{fan_et_al:LIPIcs.MFCS.2016.37,
author = {Fan, Chenglin and Filtser, Omrit and Katz, Matthew J. and Zhu, Binhai},
title = {{On the General Chain Pair Simplification Problem}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {37:1--37:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.37},
URN = {urn:nbn:de:0030-drops-64510},
doi = {10.4230/LIPIcs.MFCS.2016.37},
annote = {Keywords: chain simplification, discrete Frechet distance, dynamic programming, geometric arrangements, protein structural resemblance}
}
Document
Computing DAWGs and Minimal Absent Words in Linear Time for Integer Alphabets
Abstract
The directed acyclic word graph (DAWG) of a string y is the smallest (partial) DFA which recognizes all suffixes of y and has only O(n) nodes and edges. We present the first O(n)-time algorithm for computing the DAWG of a given string y of length n over an integer alphabet of polynomial size in n. We also show that a straightforward modification to our DAWG construction algorithm leads to the first O(n)-time algorithm for constructing the affix tree of a given string y over an integer alphabet. Affix trees are a text indexing structure supporting bidirectional pattern searches. As an application to our O(n)-time DAWG construction algorithm, we show that the set MAW(y) of all minimal absent words of y can be computed in optimal O(n + |MAW(y)|) time and O(n) working space for integer alphabets.
Cite as
Yuta Fujishige, Yuki Tsujimaru, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Computing DAWGs and Minimal Absent Words in Linear Time for Integer Alphabets. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{fujishige_et_al:LIPIcs.MFCS.2016.38,
author = {Fujishige, Yuta and Tsujimaru, Yuki and Inenaga, Shunsuke and Bannai, Hideo and Takeda, Masayuki},
title = {{Computing DAWGs and Minimal Absent Words in Linear Time for Integer Alphabets}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {38:1--38:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.38},
URN = {urn:nbn:de:0030-drops-64528},
doi = {10.4230/LIPIcs.MFCS.2016.38},
annote = {Keywords: string algorithms, DAWGs, suffix trees, minimal absent words}
}
Document
On Planar Valued CSPs
Abstract
We study the computational complexity of planar valued constraint satisfaction problems (VCSPs). First, we show that intractable Boolean VCSPs have to be self-complementary to be tractable in the planar setting, thus extending a corresponding result of Dvorak and Kupec [ICALP'15] from CSPs to VCSPs. Second, we give a complete complexity classification of conservative planar VCSPs on arbitrary finite domains. As it turns out, in this case planarity does not lead to any new tractable cases, and thus our classification is a sharpening of the classification of conservative VCSPs by Kolmogorov and Zivny [JACM'13].
Cite as
Peter Fulla and Stanislav Zivny. On Planar Valued CSPs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 39:1-39:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{fulla_et_al:LIPIcs.MFCS.2016.39,
author = {Fulla, Peter and Zivny, Stanislav},
title = {{On Planar Valued CSPs}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {39:1--39:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.39},
URN = {urn:nbn:de:0030-drops-64537},
doi = {10.4230/LIPIcs.MFCS.2016.39},
annote = {Keywords: constraint satisfaction, valued constraint satisfaction, planarity, polymorphisms, multimorphisms}
}
Document
Determining Sets of Quasiperiods of Infinite Words
Abstract
A word is quasiperiodic if it can be obtained by concatenations and overlaps of a smaller word, called a quasiperiod. Based on links between quasiperiods, right special factors and square factors, we introduce a method to determine the set of quasiperiods of a given right infinite word. Then we study the structure of the sets of quasiperiods of right infinite words and, using our method, we provide examples of right infinite words with extremal sets of quasiperiods (no quasiperiod is quasiperiodic, all quasiperiods except one are quasiperiodic, ...). Our method is also used to provide a short proof of a recent characterization of quasiperiods of the Fibonacci word. Finally we extend this result to a new characterization of standard Sturmian words using a property of their sets of quasiperiods.
Cite as
Guilhem Gamard and Gwenaël Richomme. Determining Sets of Quasiperiods of Infinite Words. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 40:1-40:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{gamard_et_al:LIPIcs.MFCS.2016.40,
author = {Gamard, Guilhem and Richomme, Gwena\"{e}l},
title = {{Determining Sets of Quasiperiods of Infinite Words}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {40:1--40:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.40},
URN = {urn:nbn:de:0030-drops-64540},
doi = {10.4230/LIPIcs.MFCS.2016.40},
annote = {Keywords: combinatorics on Words, quasiperiodicity, Sturmian words}
}
Document
On the Complexity Landscape of Connected f-Factor Problems
Abstract
Given an n-vertex graph G and a function f:V(G) -> {0, ..., n-1}, an f-factor is a subgraph H of G such that deg_H(v)=f(v) for every vertex v in V(G); we say that H is a connected f-factor if, in addition, the subgraph H is connected. A classical result of Tutte (1954) is the polynomial time algorithm to check whether a given graph has a specified f-factor. However, checking for the presence of a connected f-factor is easily seen to generalize Hamiltonian Cycle and hence is NP-complete. In fact, the Connected f-Factor problem remains NP-complete even when f(v) is at least n^epsilon for each vertex v and epsilon<1; on the other side of the spectrum, the problem was known to be polynomial-time solvable when f(v) is at least n/3 for every vertex v.
In this paper, we extend this line of work and obtain new complexity results based on restricting the function f. In particular, we show that when f(v) is required to be at least n/(log n)^c, the problem can be solved in quasi-polynomial time in general and in randomized polynomial time if c <= 1. We also show that when c>1, the problem is NP-intermediate.
Cite as
Robert Ganian, N. S. Narayanaswamy, Sebastian Ordyniak, C. S. Rahul, and M. S. Ramanujan. On the Complexity Landscape of Connected f-Factor Problems. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 41:1-41:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{ganian_et_al:LIPIcs.MFCS.2016.41,
author = {Ganian, Robert and Narayanaswamy, N. S. and Ordyniak, Sebastian and Rahul, C. S. and Ramanujan, M. S.},
title = {{On the Complexity Landscape of Connected f-Factor Problems}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {41:1--41:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.41},
URN = {urn:nbn:de:0030-drops-65013},
doi = {10.4230/LIPIcs.MFCS.2016.41},
annote = {Keywords: f-factors, connected f-factors, quasi-polynomial time algorithms, randomized algorithms}
}
Document
On Existential MSO and its Relation to ETH
Abstract
Impagliazzo et al. proposed a framework, based on the logic fragment defining the complexity class SNP, to identify problems that are equivalent to k-CNF-Sat modulo subexponential-time reducibility (serf-reducibility). The subexponential-time solvability of any of these problems implies the failure of the Exponential Time Hypothesis (ETH). In this paper, we extend the framework of Impagliazzo et al., and identify a larger set of problems that are equivalent to k-CNF-Sat modulo serf-reducibility. We propose a complexity class, referred to as Linear Monadic NP, that consists of all problems expressible in existential monadic second order logic whose expressions have a linear measure in terms of a complexity parameter, which is usually the universe size of the problem.
This research direction can be traced back to Fagin's celebrated theorem stating that NP coincides with the class of problems expressible in existential second order logic. Monadic NP, a well-studied class in the literature, is the restriction of the aforementioned logic fragment to existential monadic second order logic. The proposed class Linear Monadic NP is then the restriction of Monadic NP to problems whose expressions have linear measure in the complexity parameter.
We show that Linear Monadic NP includes many natural complete problems such as the satisfiability of linear-size circuits, dominating set, independent dominating set, and perfect code. Therefore, for any of these problems, its subexponential-time solvability is equivalent to the failure of ETH. We prove, using logic games, that the aforementioned problems are inexpressible in the monadic fragment of SNP, and hence, are not captured by the framework of Impagliazzo et al. Finally, we show that Feedback Vertex Set is inexpressible in existential monadic second order logic, and hence is not in Linear Monadic NP, and investigate the existence of certain reductions between Feedback Vertex Set (and variants of it) and 3-CNF-Sat.
Cite as
Robert Ganian, Ronald de Haan, Iyad Kanj, and Stefan Szeider. On Existential MSO and its Relation to ETH. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{ganian_et_al:LIPIcs.MFCS.2016.42,
author = {Ganian, Robert and de Haan, Ronald and Kanj, Iyad and Szeider, Stefan},
title = {{On Existential MSO and its Relation to ETH}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {42:1--42:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.42},
URN = {urn:nbn:de:0030-drops-64556},
doi = {10.4230/LIPIcs.MFCS.2016.42},
annote = {Keywords: exponential time hypothesis (ETH), monadic second order logic, subexponential time complexity, serf-reducibility, logic games}
}
Document
Programming Biomolecules That Fold Greedily During Transcription
Abstract
We introduce and study the computational power of Oritatami, a theoretical model to explore greedy molecular folding, by which a molecule begins to fold before awaiting the end of its production. This model is inspired by a recent experimental work demonstrating the construction of shapes at the nanoscale by folding an RNA molecule during its transcription from an engineered sequence of synthetic DNA.
An important challenge of this model, also encountered in experiments, is to get a single sequence to fold into different shapes, depending on the surrounding molecules. Another big challenge is that not all parts of the sequence are meaningful for all possible inputs. Hence, to prevent them from interfering with subsequent operations in the Oritatami folding pathway we must structure the unused portions of the sequence depending on the context in which it folds.
Next, we introduce general design techniques to solve these challenges and program molecules. Our main result in this direction is an algorithm that is time linear in the sequence length that finds a rule for folding the sequence deterministically into a prescribed set of shapes, dependent on its local environment. This shows that the corresponding problem is fixed-parameter tractable, although we also prove it NP-complete in the number of possible environments.
Cite as
Cody Geary, Pierre-Etienne Meunier, Nicolas Schabanel, and Shinnosuke Seki. Programming Biomolecules That Fold Greedily During Transcription. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{geary_et_al:LIPIcs.MFCS.2016.43,
author = {Geary, Cody and Meunier, Pierre-Etienne and Schabanel, Nicolas and Seki, Shinnosuke},
title = {{Programming Biomolecules That Fold Greedily During Transcription}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {43:1--43:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.43},
URN = {urn:nbn:de:0030-drops-64567},
doi = {10.4230/LIPIcs.MFCS.2016.43},
annote = {Keywords: natural computing, self-assembly, molecular folding}
}
Document
Connected Reversible Mealy Automata of Prime Size Cannot Generate Infinite Burnside Groups
Abstract
The simplest example of an infinite Burnside group arises in the class of automaton groups. However there is no known example of such a group generated by a reversible Mealy automaton. It has been proved that, for a connected automaton of size at most 3, or when the automaton is not bireversible, the generated group cannot be Burnside infinite. In this paper, we extend these results to automata with bigger stateset, proving that, if a connected reversible automaton has a prime number of states, it cannot generate an infinite Burnside group.
Cite as
Thibault Godin and Ines Klimann. Connected Reversible Mealy Automata of Prime Size Cannot Generate Infinite Burnside Groups. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{godin_et_al:LIPIcs.MFCS.2016.44,
author = {Godin, Thibault and Klimann, Ines},
title = {{Connected Reversible Mealy Automata of Prime Size Cannot Generate Infinite Burnside Groups}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {44:1--44:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.44},
URN = {urn:nbn:de:0030-drops-64570},
doi = {10.4230/LIPIcs.MFCS.2016.44},
annote = {Keywords: Burnside problem, automaton groups, reversibility, orbit trees}
}
Document
Circuit Size Lower Bounds and #SAT Upper Bounds Through a General Framework
Abstract
Most of the known lower bounds for binary Boolean circuits with unrestricted depth are proved by the gate elimination method. The most efficient known algorithms for the #SAT problem on binary Boolean circuits use similar case analyses to the ones in gate elimination. Chen and Kabanets recently showed that the known case analyses can also be used to prove average case circuit lower bounds, that is, lower bounds on the size of approximations of an explicit function.
In this paper, we provide a general framework for proving worst/average case lower bounds for circuits and upper bounds for #SAT that is built on ideas of Chen and Kabanets. A proof in such a framework goes as follows. One starts by fixing three parameters: a class of circuits, a circuit complexity measure, and a set of allowed substitutions. The main ingredient of a proof goes as follows: by going through a number of cases, one shows that for any circuit from the given class, one can find an allowed substitution such that the given measure of the circuit reduces by a sufficient amount. This case analysis immediately implies an upper bound for #SAT. To~obtain worst/average case circuit complexity lower bounds one needs to present an explicit construction of a function that is a disperser/extractor for the class of sources defined by the set of substitutions under consideration.
We show that many known proofs (of circuit size lower bounds and upper bounds for #SAT) fall into this framework.
Using this framework, we prove the following new bounds: average case lower bounds of 3.24n and 2.59n for circuits over U_2 and B_2, respectively (though the lower bound for the basis B_2 is given for a quadratic disperser whose explicit construction is not currently known), and faster than 2^n #SAT-algorithms for circuits over U_2 and B_2 of size at most 3.24n and 2.99n, respectively. Here by B_2 we mean the set of all bivariate Boolean functions, and by U_2 the set of all bivariate Boolean functions except for parity and its complement.
Cite as
Alexander Golovnev, Alexander S. Kulikov, Alexander V. Smal, and Suguru Tamaki. Circuit Size Lower Bounds and #SAT Upper Bounds Through a General Framework. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{golovnev_et_al:LIPIcs.MFCS.2016.45,
author = {Golovnev, Alexander and Kulikov, Alexander S. and Smal, Alexander V. and Tamaki, Suguru},
title = {{Circuit Size Lower Bounds and #SAT Upper Bounds Through a General Framework}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {45:1--45:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.45},
URN = {urn:nbn:de:0030-drops-64588},
doi = {10.4230/LIPIcs.MFCS.2016.45},
annote = {Keywords: circuit complexity, lower bounds, exponential time algorithms, satisfiability}
}
Document
On the Limits of Gate Elimination
Abstract
Although a simple counting argument shows the existence of Boolean functions of exponential circuit complexity, proving superlinear circuit lower bounds for explicit functions seems to be out of reach of the current techniques. There has been a (very slow) progress in proving linear lower bounds with the latest record of 3 1/86*n-o(n). All known lower bounds are based on the so-called gate elimination technique. A typical gate elimination argument shows that it is possible to eliminate several gates from an optimal circuit by making one or several substitutions to the input variables and repeats this inductively. In this note we prove that this method cannot achieve linear bounds of cn beyond a certain constant c, where c depends only on the number of substitutions made at a single step of the induction.
Cite as
Alexander Golovnev, Edward A. Hirsch, Alexander Knop, and Alexander S. Kulikov. On the Limits of Gate Elimination. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{golovnev_et_al:LIPIcs.MFCS.2016.46,
author = {Golovnev, Alexander and Hirsch, Edward A. and Knop, Alexander and Kulikov, Alexander S.},
title = {{On the Limits of Gate Elimination}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {46:1--46:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.46},
URN = {urn:nbn:de:0030-drops-64593},
doi = {10.4230/LIPIcs.MFCS.2016.46},
annote = {Keywords: circuit complexity, lower bounds, gate elimination}
}
Document
Algebraic Problems Equivalent to Beating Exponent 3/2 for Polynomial Factorization over Finite Fields
Abstract
The fastest known algorithm for factoring univariate polynomials over finite fields is the Kedlaya-Umans (fast modular composition) implementation of the Kaltofen-Shoup algorithm. It is randomized and takes ~O(n^{3/2}*log(q)+n*log^2(q)) time to factor polynomials of degree n over the finite field F_q with q elements. A significant open problem is if the 3/2 exponent can be improved. We study a collection of algebraic problems and establish a web of reductions between them. A consequence is that an algorithm for any one of these problems with exponent better than 3/2 would yield an algorithm for polynomial factorization with exponent better than 3/2.
Cite as
Zeyu Guo, Anand Kumar Narayanan, and Chris Umans. Algebraic Problems Equivalent to Beating Exponent 3/2 for Polynomial Factorization over Finite Fields. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 47:1-47:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{guo_et_al:LIPIcs.MFCS.2016.47,
author = {Guo, Zeyu and Narayanan, Anand Kumar and Umans, Chris},
title = {{Algebraic Problems Equivalent to Beating Exponent 3/2 for Polynomial Factorization over Finite Fields}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {47:1--47:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.47},
URN = {urn:nbn:de:0030-drops-64609},
doi = {10.4230/LIPIcs.MFCS.2016.47},
annote = {Keywords: algorithms, complexity, finite fields, polynomials, factorization}
}
Document
On Synchronizing Colorings and the Eigenvectors of Digraphs
Abstract
An automaton is synchronizing if there exists a word that sends all states of the automaton to a single state. A coloring of a digraph with a fixed out-degree k is a distribution of k labels over the edges resulting in a deterministic finite automaton. The famous road coloring theorem states that every primitive digraph has a synchronizing coloring. We study recent conjectures claiming that the number of synchronizing colorings is large in the worst and average cases.
Our approach is based on the spectral properties of the adjacency matrix A(G) of a digraph G. Namely, we study the relation between the number of synchronizing colorings of G and the structure of the dominant eigenvector v of A(G). We show that a vector v has no partition of coordinates into blocks of equal sum if and only if all colorings of the digraphs associated with v are synchronizing. Furthermore, if for each b there exists at most one partition of the coordinates of v into blocks summing up to b, and the total number of partitions is equal to s, then the fraction of synchronizing colorings among all colorings of G is at least (k-s)/k. We also give a combinatorial interpretation of some known results concerning an upper bound on the minimal length of synchronizing words in terms of v.
Cite as
Vladimir V. Gusev and Elena V. Pribavkina. On Synchronizing Colorings and the Eigenvectors of Digraphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 48:1-48:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{gusev_et_al:LIPIcs.MFCS.2016.48,
author = {Gusev, Vladimir V. and Pribavkina, Elena V.},
title = {{On Synchronizing Colorings and the Eigenvectors of Digraphs}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {48:1--48:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.48},
URN = {urn:nbn:de:0030-drops-64611},
doi = {10.4230/LIPIcs.MFCS.2016.48},
annote = {Keywords: the road coloring problem, synchronizing automata, edge-colorings of digraphs, Perron-Frobenius eigenvector, primitive digraphs}
}
Document
Competitive Packet Routing with Priority Lists
Abstract
In competitive packet routing games, packets are routed selfishly through a network and scheduling policies at edges determine which packages are forwarded first if there is not enough capacity on an edge to forward all packages at once. We analyze the impact of priority lists on the worst-case quality of pure Nash equilibria. A priority list is an ordered list of players that may or may not depend on the edge. Whenever the number of packets entering an edge exceeds the inflow capacity, packets are processed in list order. We derive several new bounds on the price of anarchy and stability for global and local priority policies. We also consider the question of the complexity of computing an optimal priority list. It turns out that even for very restricted cases, i.e., for routing on a tree, the computation of an optimal priority list is APX-hard.
Cite as
Tobias Harks, Britta Peis, Daniel Schmand, and Laura Vargas Koch. Competitive Packet Routing with Priority Lists. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{harks_et_al:LIPIcs.MFCS.2016.49,
author = {Harks, Tobias and Peis, Britta and Schmand, Daniel and Vargas Koch, Laura},
title = {{Competitive Packet Routing with Priority Lists}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {49:1--49:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.49},
URN = {urn:nbn:de:0030-drops-64622},
doi = {10.4230/LIPIcs.MFCS.2016.49},
annote = {Keywords: packet routing, Nash equilibrium, price of anarchy, priority policy, complexity}
}
Document
The Ground-Set-Cost Budgeted Maximum Coverage Problem
Abstract
We study the following natural variant of the budgeted maximum coverage problem: We are given a budget B and a hypergraph G = (V, E), where each vertex has a non-negative cost and a non-negative profit. The goal is to select a set of hyperedges T subseteq E such that the total cost of the vertices covered by T is at most B and the total profit of all covered vertices is maximized. Besides being a natural generalization of the well-studied maximum coverage problem, our motivation for investigating this problem originates from its application in the context of bid optimization in sponsored search auctions, such as Google AdWords.
It is easily seen that this problem is strictly harder than budgeted max coverage, which means that the problem is (1-1/e)-inapproximable. The difference of our problem to the budgeted maximum coverage problem is that the costs are associated with the covered vertices instead of the selected hyperedges. As it turns out, this difference refutes the applicability of standard greedy approaches which are used to obtain constant factor approximation algorithms for several other variants of the maximum coverage problem. Our main results are as follows:
- We obtain a (1 - 1/sqrt(e))/2-approximation algorithm for graphs.
- We derive a fully polynomial-time approximation scheme (FPTAS) if the incidence graph of the hypergraph is a forest (i.e., the hypergraph is Berge-acyclic). We also extend this result to incidence graphs with a fixed-size feedback hyperedge node set.
- We give a (1-epsilon)/(2d^2)-approximation algorithm for every epsilon > 0, where d is the maximum degree of a vertex in the hypergraph.
Cite as
Irving van Heuven van Staereling, Bart de Keijzer, and Guido Schäfer. The Ground-Set-Cost Budgeted Maximum Coverage Problem. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 50:1-50:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{vanheuvenvanstaereling_et_al:LIPIcs.MFCS.2016.50,
author = {van Heuven van Staereling, Irving and de Keijzer, Bart and Sch\"{a}fer, Guido},
title = {{The Ground-Set-Cost Budgeted Maximum Coverage Problem}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {50:1--50:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.50},
URN = {urn:nbn:de:0030-drops-65020},
doi = {10.4230/LIPIcs.MFCS.2016.50},
annote = {Keywords: maximum coverage problem, approximation algorithms, hypergraphs, submodular optimization, sponsored search}
}
Document
Computational and Proof Complexity of Partial String Avoidability
Abstract
The partial string avoidability problem, also known as partial word avoidability, is stated as follows: given a finite set of strings with possible ``holes'' (undefined symbols), determine whether there exists any two-sided infinite string containing no substrings from this set, assuming that a hole matches every symbol.
The problem is known to be NP-hard and in PSPACE, and this paper establishes its PSPACE-completeness.
Next, string avoidability over the binary alphabet is interpreted as a version of conjunctive normal form (CNF) satisfiability problem (SAT), with each clause having infinitely many shifted variants.
Non-satisfiability of these formulas can be proved using variants of classical propositional proof systems, augmented with derivation rules for shifting constraints (such as clauses, inequalities, polynomials, etc).
Two results on their proof complexity are established.
First, there is a particular formula that has a short refutation in Resolution with shift, but requires classical proofs of exponential size (Resolution, Cutting Plane, Polynomial Calculus, etc.).
At the same time, exponential lower bounds for shifted versions of classical proof systems are established.
Cite as
Dmitry Itsykson, Alexander Okhotin, and Vsevolod Oparin. Computational and Proof Complexity of Partial String Avoidability. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 51:1-51:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{itsykson_et_al:LIPIcs.MFCS.2016.51,
author = {Itsykson, Dmitry and Okhotin, Alexander and Oparin, Vsevolod},
title = {{Computational and Proof Complexity of Partial String Avoidability}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {51:1--51:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.51},
URN = {urn:nbn:de:0030-drops-64637},
doi = {10.4230/LIPIcs.MFCS.2016.51},
annote = {Keywords: partial strings, partial words, avoidability, proof complexity, PSPACE-completeness}
}
Document
Deciding Semantic Finiteness of Pushdown Processes and First-Order Grammars w.r.t. Bisimulation Equivalence
Abstract
The problem if a given configuration of a pushdown automaton (PDA) is
bisimilar with some (unspecified) finite-state process is shown to be
decidable. The decidability is proven in the framework of first-order grammars, which are given by finite sets of labelled rules that rewrite roots of first-order terms. The framework is equivalent to PDA where also deterministic popping epsilon-steps are allowed, i.e. to the model for which Senizergues showed an involved procedure deciding bisimilarity (FOCS 1998). Such a procedure is here used as a black-box part of the algorithm. For deterministic PDA the regularity problem was shown decidable by Valiant (JACM 1975) but the decidability question for nondeterministic PDA, answered positively here, had been open (as indicated, e.g., by Broadbent and Goeller, FSTTCS 2012).
Cite as
Petr Jancar. Deciding Semantic Finiteness of Pushdown Processes and First-Order Grammars w.r.t. Bisimulation Equivalence. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 52:1-52:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{jancar:LIPIcs.MFCS.2016.52,
author = {Jancar, Petr},
title = {{Deciding Semantic Finiteness of Pushdown Processes and First-Order Grammars w.r.t. Bisimulation Equivalence}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {52:1--52:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.52},
URN = {urn:nbn:de:0030-drops-64649},
doi = {10.4230/LIPIcs.MFCS.2016.52},
annote = {Keywords: pushdown processes, first-order grammars, bisimulation, regularity}
}
Document
Minimal Phylogenetic Supertrees and Local Consensus Trees
Abstract
The problem of constructing a minimally resolved phylogenetic supertree (i.e., having the smallest possible number of internal nodes) that contains all of the rooted triplets from a consistent set R is known to be NP-hard. In this paper, we prove that constructing a phylogenetic tree consistent with R that contains the minimum number of additional rooted triplets is also NP-hard, and develop exact, exponential-time algorithms for both problems. The new algorithms are applied to construct two variants of the local consensus tree;
for any set S of phylogenetic trees over some leaf label set L,
this gives a minimal phylogenetic tree over L that contains every
rooted triplet present in all trees in S, where ``minimal'' means either having the smallest possible number of internal nodes or
the smallest possible number of rooted triplets. The second variant generalizes the RV-II tree, introduced by Kannan, Warnow, and Yooseph in 1998.
Cite as
Jesper Jansson and Wing-Kin Sung. Minimal Phylogenetic Supertrees and Local Consensus Trees. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 53:1-53:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{jansson_et_al:LIPIcs.MFCS.2016.53,
author = {Jansson, Jesper and Sung, Wing-Kin},
title = {{Minimal Phylogenetic Supertrees and Local Consensus Trees}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {53:1--53:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.53},
URN = {urn:nbn:de:0030-drops-64653},
doi = {10.4230/LIPIcs.MFCS.2016.53},
annote = {Keywords: phylogenetic tree, rooted triplet, local consensus, minimal supertree, computational complexity, bioinformatics}
}
Document
Quantum Communication Complexity of Distributed Set Joins
Abstract
Computing set joins of two inputs is a common task in database theory. Recently, Van Gucht, Williams, Woodruff and Zhang [PODS 2015] considered the complexity of such problems in the natural model of (classical) two-party communication complexity and obtained tight bounds for the complexity of several important distributed set joins.
In this paper we initiate the study of the quantum communication complexity of distributed set joins. We design a quantum protocol for distributed Boolean matrix multiplication, which corresponds to computing the composition join of two databases, showing that the product of two n times n Boolean matrices, each owned by one of two respective parties, can be computed with widetilde-O(sqrt{n} ell^{3/4}) qubits of communication, where ell denotes the number of non-zero entries of the product. Since Van Gucht et al. showed that the classical communication complexity of this problem is widetilde-Theta(n sqrt{ell}), our quantum algorithm outperforms classical protocols whenever the output matrix is sparse. We also show a quantum lower bound and a matching classical upper bound on the communication complexity of distributed matrix multiplication over F_2.
Besides their applications to database theory, the communication complexity of set joins is interesting due to its connections to direct product theorems in communication complexity. In this work we also introduce a notion of all-pairs product theorem, and relate this notion to standard direct product theorems in communication complexity.
Cite as
Stacey Jeffery and François Le Gall. Quantum Communication Complexity of Distributed Set Joins. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 54:1-54:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{jeffery_et_al:LIPIcs.MFCS.2016.54,
author = {Jeffery, Stacey and Le Gall, Fran\c{c}ois},
title = {{Quantum Communication Complexity of Distributed Set Joins}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {54:1--54:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.54},
URN = {urn:nbn:de:0030-drops-64663},
doi = {10.4230/LIPIcs.MFCS.2016.54},
annote = {Keywords: quantum communication complexity, distributed quantum computing, database joins}
}
Document
On the Voting Time of the Deterministic Majority Process
Abstract
In the deterministic binary majority process we are given a simple graph where each node has one out of two initial opinions. In every round, each node adopts the majority opinion among its neighbors. It is known that this process always converges in O(|E|) rounds to a two-periodic state in which every node either keeps its opinion or changes it in every round.
It has been shown by Frischknecht, Keller, and Wattenhofer (2013) that the O(|E|) bound on the convergence time of the deterministic binary majority process is even for dense graphs tight. However, in many graphs such as the complete graph the process converges in just
a constant number of rounds from any initial opinion assignment.
We show that it is NP-hard to decide whether there exists an initial opinion assignment for which it takes more than k rounds to converge to the two-periodic stable state, for a given integer k. We then give a new upper bound on the voting time of the deterministic binary majority process. Our bound can be computed in linear time by carefully exploiting the structure of the potential function by Goles and Olivos. We identify certain modules of a graph G to obtain a new graph G^Delta. This new graph G^Delta has the property that the worst-case convergence time of G^Delta is an upper bound on that of G. Our new bounds asymptotically improve the best known bounds for various graph classes.
Cite as
Dominik Kaaser, Frederik Mallmann-Trenn, and Emanuele Natale. On the Voting Time of the Deterministic Majority Process. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{kaaser_et_al:LIPIcs.MFCS.2016.55,
author = {Kaaser, Dominik and Mallmann-Trenn, Frederik and Natale, Emanuele},
title = {{On the Voting Time of the Deterministic Majority Process}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {55:1--55:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.55},
URN = {urn:nbn:de:0030-drops-64675},
doi = {10.4230/LIPIcs.MFCS.2016.55},
annote = {Keywords: distributed voting, majority rule}
}
Document
Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs
Abstract
We present space-efficient algorithms for computing cut vertices in a given graph with n vertices and m edges in linear time using O(n+min{m,n log log n}) bits. With the same time and using O(n+m) bits, we can compute the biconnected components of a graph. We use this result to show an algorithm for the recognition of (maximal) outerplanar graphs in O(n log log n) time using O(n) bits.
Cite as
Frank Kammer, Dieter Kratsch, and Moritz Laudahn. Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 56:1-56:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{kammer_et_al:LIPIcs.MFCS.2016.56,
author = {Kammer, Frank and Kratsch, Dieter and Laudahn, Moritz},
title = {{Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {56:1--56:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.56},
URN = {urn:nbn:de:0030-drops-64683},
doi = {10.4230/LIPIcs.MFCS.2016.56},
annote = {Keywords: graph algorithms, space efficiency, cut vertices, maximal outerplanar graphs}
}
Document
Multi-Party Protocols, Information Complexity and Privacy
Abstract
We introduce the new measure of Public Information Complexity (PIC), as a tool for the study of multi-party computation protocols, and of quantities such as their communication complexity, or the amount of randomness they require in the context of information-theoretic private computations. We are able to use this measure directly in the natural asynchronous message-passing peer-to-peer model and show a number of interesting properties and applications of our new notion:
the Public Information Complexity is a lower bound on the Communication Complexity and an upper bound on the Information Complexity; the difference between the Public Information Complexity and the Information Complexity provides a lower bound on the amount of randomness used in a protocol; any communication protocol can be compressed to its Public Information Cost; an explicit calculation of the zero-error Public Information Complexity of the k-party, n-bit Parity function, where a player outputs the bit-wise parity of the inputs. The latter result establishes that the amount of randomness needed for a private protocol that computes this function is Omega(n).
Cite as
Iordanis Kerenidis, Adi Rosén, and Florent Urrutia. Multi-Party Protocols, Information Complexity and Privacy. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 57:1-57:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{kerenidis_et_al:LIPIcs.MFCS.2016.57,
author = {Kerenidis, Iordanis and Ros\'{e}n, Adi and Urrutia, Florent},
title = {{Multi-Party Protocols, Information Complexity and Privacy}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {57:1--57:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.57},
URN = {urn:nbn:de:0030-drops-64696},
doi = {10.4230/LIPIcs.MFCS.2016.57},
annote = {Keywords: multi-party protocols, information theory, communication complexity, multi-party private computation (MPC), randomness}
}
Document
Dividing by Zero - How Bad Is It, Really?
Abstract
In computable analysis testing a real number for being zero is a fundamental example of a non-computable task. This causes problems for division: We cannot ensure that the number we want to divide by is not zero. In many cases, any real number would be an acceptable outcome if the divisor is zero - but even this cannot be done in a computable way.
In this note we investigate the strength of the computational problem Robust division: Given a pair of real numbers, the first not greater than the other, output their quotient if well-defined and any real number else. The formal framework is provided by Weihrauch reducibility. One particular result is that having later calls to the problem depending on the outcomes of earlier ones is strictly more powerful than performing all calls concurrently. However, having a nesting depths of two already provides the full power. This solves an open problem raised at a recent Dagstuhl meeting on Weihrauch reducibility.
As application for Robust division, we show that it suffices to execute Gaussian elimination.
Cite as
Takayuki Kihara and Arno Pauly. Dividing by Zero - How Bad Is It, Really?. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{kihara_et_al:LIPIcs.MFCS.2016.58,
author = {Kihara, Takayuki and Pauly, Arno},
title = {{Dividing by Zero - How Bad Is It, Really?}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {58:1--58:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.58},
URN = {urn:nbn:de:0030-drops-64702},
doi = {10.4230/LIPIcs.MFCS.2016.58},
annote = {Keywords: computable analysis, Weihrauch reducibility, recursion theory, linear algebra}
}
Document
Advice Complexity of the Online Induced Subgraph Problem
Abstract
Several well-studied graph problems aim to select a largest (or smallest) induced subgraph with a given property of the input graph. Examples include maximum independent set, maximum planar graph, maximum clique, minimum feedback vertex set, and many others. In online versions of these problems, the vertices of the graph are presented in an adversarial order, and with each vertex, the online algorithm must irreversibly decide whether to include it into the constructed subgraph, based only on the subgraph induced by the vertices presented so far. We study the properties that are common to all these problems by investigating a generalized problem: for an arbitrary but fixed hereditary property pi, find some maximal induced subgraph having pi. We investigate this problem from the point of view of advice complexity, i.e., we ask how some additional information about the yet unrevealed parts of the input can influence the solution quality. We evaluate the information in a quantitative way by considering the best possible advice of given size that describes the unknown input. Using a result from Boyar et al. [STACS 2015, LIPIcs 30], we give a tight trade-off relationship stating that, for inputs of length n, roughly n/c bits of advice are both needed and sufficient to obtain a solution with competitive ratio c, regardless of the choice of pi, for any c (possibly a function of n). This complements the results from Bartal et al. [SIAM Journal on Computing 36(2), 2006] stating that, without any advice, even a randomized algorithm cannot achieve a competitive ratio better than Omega(n^{1-log_{4}3-o(1)}). Surprisingly, for a given cohereditary property pi and the objective to find a minimum subgraph having pi, the advice complexity varies significantly with the choice of pi. We also consider a preemptive online model, inspired by some applications mainly in networking and scheduling, where the decision of the algorithm is not completely irreversible. In particular, the algorithm may discard some vertices previously assigned to the constructed set, but discarded vertices cannot be reinserted into the set. We show that, for the maximum induced subgraph problem, preemption does not significantly help by giving a lower bound of Omega(n/(c^2log c)) on the bits of advice that are needed to obtain
competitive ratio c, where c is any increasing function bounded from above by sqrt(n/log n). We also give a linear lower bound for c close to 1.
Cite as
Dennis Komm, Rastislav Královic, Richard Královic, and Christian Kudahl. Advice Complexity of the Online Induced Subgraph Problem. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 59:1-59:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{komm_et_al:LIPIcs.MFCS.2016.59,
author = {Komm, Dennis and Kr\'{a}lovic, Rastislav and Kr\'{a}lovic, Richard and Kudahl, Christian},
title = {{Advice Complexity of the Online Induced Subgraph Problem}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {59:1--59:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.59},
URN = {urn:nbn:de:0030-drops-64713},
doi = {10.4230/LIPIcs.MFCS.2016.59},
annote = {Keywords: online algorithms, advice complexity, induced subgraph problem}
}
Document
Decidability of Predicate Logics with Team Semantics
Abstract
We study the complexity of predicate logics based on team semantics.
We show that the satisfiability problems of two-variable independence logic and inclusion logic are both NEXPTIME-complete. Furthermore, we show that the validity problem of two-variable dependence logic is undecidable, thereby solving an open problem from the team semantics literature. We also briefly analyse the complexity of the Bernays-Schoenfinkel-Ramsey prefix classes of dependence logic.
Cite as
Juha Kontinen, Antti Kuusisto, and Jonni Virtema. Decidability of Predicate Logics with Team Semantics. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{kontinen_et_al:LIPIcs.MFCS.2016.60,
author = {Kontinen, Juha and Kuusisto, Antti and Virtema, Jonni},
title = {{Decidability of Predicate Logics with Team Semantics}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {60:1--60:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.60},
URN = {urn:nbn:de:0030-drops-64726},
doi = {10.4230/LIPIcs.MFCS.2016.60},
annote = {Keywords: team semantics, dependence logic, complexity, two-variable logic}
}
Document
On the Complexity of Universality for Partially Ordered NFAs
Abstract
Partially ordered nondeterminsitic finite automata (poNFAs) are NFAs whose transition relation induces a partial order on states, i.e., for which cycles occur only in the form of self-loops on a single state. A poNFA is universal if it accepts all words over its input alphabet.
Deciding universality is \PSpace-complete for poNFAs, and we show that this remains true even when restricting to a fixed alphabet. This is nontrivial since standard encodings of alphabet symbols in, e.g., binary can turn self-loops into longer cycles. A lower coNP-complete complexity bound can be obtained if we require that all self-loops in the poNFA are deterministic, in the sense that the symbol read in the loop cannot occur in any other transition from that state. We find that such restricted poNFAs (rpoNFAs) characterise the class of R-trivial languages, and we establish the complexity of deciding if the language of an NFA is R-trivial. Nevertheless, the limitation to fixed alphabets turns out to be essential even in the restricted case: deciding universality of rpoNFAs with unbounded alphabets is PSPACE-complete. Our results also prove the complexity of the inclusion and equivalence problems, since universality provides the lower bound, while the upper bound is mostly known or proved in the paper.
Cite as
Markus Krötzsch, Tomás Masopust, and Michaël Thomazo. On the Complexity of Universality for Partially Ordered NFAs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 61:1-61:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{krotzsch_et_al:LIPIcs.MFCS.2016.61,
author = {Kr\"{o}tzsch, Markus and Masopust, Tom\'{a}s and Thomazo, Micha\"{e}l},
title = {{On the Complexity of Universality for Partially Ordered NFAs}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {61:1--61:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.61},
URN = {urn:nbn:de:0030-drops-64738},
doi = {10.4230/LIPIcs.MFCS.2016.61},
annote = {Keywords: automata, nondeterminism, partial order, universality}
}
Document
Eulerian Paths with Regular Constraints
Abstract
Labeled graphs, in which edges are labeled by letters from some alphabet Sigma, are extensively used to model many types of
relations associated with actions, costs, owners, or other
properties. Each path in a labeled graph induces a word in Sigma^*
-- the one obtained by concatenating the letters along the edges in
the path. Classical graph-theory problems give rise to new problems
that take these words into account. We introduce and study the
constrained Eulerian path problem. The input to the problem is a
Sigma-labeled graph G and a specification L \subseteq Sigma^*.
The goal is to find an Eulerian path in G that satisfies L. We
consider several classes of the problem, defined by the classes of G
and L. We focus on the case L is regular and show that while the
problem is in general NP-complete, even for very simple graphs and
specifications, there are classes that can be solved efficiently. Our
results extend work on Eulerian paths with edge-order constraints. We
also study the constrained Chinese postman problem, where
edges have costs and the goal is to find a cheapest path that contains
each edge at least once and satisfies the specification. Finally, we
define and study the Eulerian language of a graph, namely the
set of words along its Eulerian paths.
Cite as
Orna Kupferman and Gal Vardi. Eulerian Paths with Regular Constraints. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 62:1-62:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{kupferman_et_al:LIPIcs.MFCS.2016.62,
author = {Kupferman, Orna and Vardi, Gal},
title = {{Eulerian Paths with Regular Constraints}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {62:1--62:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.62},
URN = {urn:nbn:de:0030-drops-64747},
doi = {10.4230/LIPIcs.MFCS.2016.62},
annote = {Keywords: Eulerian paths, regular languages}
}
Document
On the Exact Learnability of Graph Parameters: The Case of Partition Functions
Abstract
We study the exact learnability of real valued graph parameters f which are known to be representable as partition functions which count the number of weighted homomorphisms into a graph H with vertex weights alpha and edge weights beta. M. Freedman, L. Lovasz and A. Schrijver have given a characterization of these graph parameters in terms of the k-connection matrices C(f,k) of f. Our model of learnability is based on D. Angluin's model of exact learning using membership and equivalence queries. Given such a graph parameter f, the learner can ask for the values of f for graphs of their choice, and they can formulate hypotheses in terms of the connection matrices C(f,k) of f. The teacher can accept the hypothesis as correct, or provide a counterexample consisting of a graph. Our main result shows that in this scenario, a very large class of partition functions,
the rigid partition functions, can be learned in time polynomial in the size of H and the size of the largest counterexample in the Blum-Shub-Smale model of computation over the reals with unit cost.
Cite as
Nadia Labai and Johann A. Makowsky. On the Exact Learnability of Graph Parameters: The Case of Partition Functions. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 63:1-63:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{labai_et_al:LIPIcs.MFCS.2016.63,
author = {Labai, Nadia and Makowsky, Johann A.},
title = {{On the Exact Learnability of Graph Parameters: The Case of Partition Functions}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {63:1--63:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.63},
URN = {urn:nbn:de:0030-drops-64750},
doi = {10.4230/LIPIcs.MFCS.2016.63},
annote = {Keywords: exact learning, partition function, weighted homomorphism, connection matrices}
}
Document
A Preliminary Investigation of Satisfiability Problems Not Harder than 1-in-3-SAT
Abstract
The parameterized satisfiability problem over a set of Boolean
relations Gamma (SAT(Gamma)) is the problem of determining
whether a conjunctive formula over Gamma has at least one
model. Due to Schaefer's dichotomy theorem the computational
complexity of SAT(Gamma), modulo polynomial-time reductions, has
been completely determined: SAT(Gamma) is always either tractable
or NP-complete. More recently, the problem of studying the
relationship between the complexity of the NP-complete cases of
SAT(Gamma) with restricted notions of reductions has attracted
attention. For example, Impagliazzo et al. studied the complexity of
k-SAT and proved that the worst-case time complexity increases
infinitely often for larger values of k, unless 3-SAT is solvable in
subexponential time. In a similar line of research Jonsson et al.
studied the complexity of SAT(Gamma) with algebraic tools borrowed
from clone theory and proved that there exists an NP-complete problem
SAT(R^{neq,neq,neq,01}_{1/3}) such that there cannot exist any NP-complete SAT(Gamma) problem with strictly lower worst-case time complexity: the easiest NP-complete SAT(Gamma) problem. In this paper
we are interested in classifying the NP-complete SAT(Gamma)
problems whose worst-case time complexity is lower than 1-in-3-SAT but
higher than the easiest problem SAT(R^{neq,neq,neq,01}_{1/3}). Recently it was conjectured that there only exists three satisfiability problems of this form. We prove that this conjecture does not hold and that there is an infinite number of such SAT(Gamma) problems. In the process we determine several algebraic properties of 1-in-3-SAT and related problems, which could be of independent interest for constructing exponential-time algorithms.
Cite as
Victor Lagerkvist and Biman Roy. A Preliminary Investigation of Satisfiability Problems Not Harder than 1-in-3-SAT. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 64:1-64:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{lagerkvist_et_al:LIPIcs.MFCS.2016.64,
author = {Lagerkvist, Victor and Roy, Biman},
title = {{A Preliminary Investigation of Satisfiability Problems Not Harder than 1-in-3-SAT}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {64:1--64:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.64},
URN = {urn:nbn:de:0030-drops-64769},
doi = {10.4230/LIPIcs.MFCS.2016.64},
annote = {Keywords: clone theory, universal algebra, satisfiability problems}
}
Document
Uniformization Problems for Tree-Automatic Relations and Top-Down Tree Transducers
Abstract
For a given binary relation of finite trees, we consider the
synthesis problem of deciding whether there is a deterministic
top-down tree transducer that uniformizes the relation, and
constructing such a transducer if it exists. A uniformization of a
relation is a function that is contained in the relation and has the
same domain as the relation. It is known that this problem is
decidable if the relation is a deterministic top-down tree-automatic
relation. We show that it becomes undecidable for general
tree-automatic relations (specified by non-deterministic top-down
tree automata). We also exhibit two cases for which the problem
remains decidable. If we restrict the transducers to be
path-preserving, which is a subclass of linear transducers, then the
synthesis problem is decidable for general tree-automatic
relations. If we consider relations that are finite unions of
deterministic top-down tree-automatic relations, then the problem is
decidable for synchronous transducers, which produce exactly one
output symbol in each step (but can be non-linear).
Cite as
Christof Löding and Sarah Winter. Uniformization Problems for Tree-Automatic Relations and Top-Down Tree Transducers. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 65:1-65:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{loding_et_al:LIPIcs.MFCS.2016.65,
author = {L\"{o}ding, Christof and Winter, Sarah},
title = {{Uniformization Problems for Tree-Automatic Relations and Top-Down Tree Transducers}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {65:1--65:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.65},
URN = {urn:nbn:de:0030-drops-64771},
doi = {10.4230/LIPIcs.MFCS.2016.65},
annote = {Keywords: tree transducers, tree automatic relation, uniformization}
}
Document
Two-Variable Logic over Countable Linear Orderings
Abstract
We study the class of languages of finitely-labelled countable linear orderings definable in two-variable first-order logic. We give a number of characterisations, in particular an algebraic one in terms of circle monoids, using equations. This generalises the corresponding characterisation, namely variety DA, over finite words to the countable case. A corollary is that the membership in this class is decidable: for instance given an MSO formula it is possible to check if there is an equivalent two-variable logic formula over countable linear orderings. In addition, we prove that the satisfiability problems for two-variable logic over arbitrary, countable, and scattered linear orderings are NEXPTIME-complete.
Cite as
Amaldev Manuel and A. V. Sreejith. Two-Variable Logic over Countable Linear Orderings. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 66:1-66:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{manuel_et_al:LIPIcs.MFCS.2016.66,
author = {Manuel, Amaldev and Sreejith, A. V.},
title = {{Two-Variable Logic over Countable Linear Orderings}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {66:1--66:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.66},
URN = {urn:nbn:de:0030-drops-64788},
doi = {10.4230/LIPIcs.MFCS.2016.66},
annote = {Keywords: circ-monoids, countable linear orderings, FO^2}
}
Document
Piecewise Testable Languages and Nondeterministic Automata
Abstract
A regular language is k-piecewise testable if it is a finite boolean combination of languages of the form Sigma^* a_1 Sigma^* ... Sigma^* a_n Sigma^*, where a_i in Sigma and 0 <= n <= k. Given a DFA A and k >= 0, it is an NL-complete problem to decide whether the language L(A) is piecewise testable and, for k >= 4, it is coNP-complete to decide whether the language L(A) is k-piecewise testable. It is known that the depth of the minimal DFA serves as an upper bound on k. Namely, if L(A) is piecewise testable, then it is k-piecewise testable for k equal to the depth of A. In this paper, we show that some form of nondeterminism does not violate this upper bound result. Specifically, we define a class of NFAs, called ptNFAs, that recognize piecewise testable languages and show that the depth of a ptNFA provides an (up to exponentially better) upper bound on k than the minimal DFA. We provide an application of our result, discuss the relationship between k-piecewise testability and the depth of NFAs, and study the complexity of k-piecewise testability for ptNFAs.
Cite as
Tomás Masopust. Piecewise Testable Languages and Nondeterministic Automata. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{masopust:LIPIcs.MFCS.2016.67,
author = {Masopust, Tom\'{a}s},
title = {{Piecewise Testable Languages and Nondeterministic Automata}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {67:1--67:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.67},
URN = {urn:nbn:de:0030-drops-64799},
doi = {10.4230/LIPIcs.MFCS.2016.67},
annote = {Keywords: automata, logics, languages, k-piecewise testability, nondeterminism}
}
Document
Stably Computing Order Statistics with Arithmetic Population Protocols
Abstract
In this paper we initiate the study of populations of agents with very limited capabilities that are globally able to compute order statistics of their arithmetic input values via pair-wise meetings.
To this extent, we introduce the Arithmetic Population Protocol (APP) model, embarking from the well known Population Protocol (PP) model and inspired by two recent papers in which states are treated as integer numbers. In the APP model, every agent has a state from a set Q of states, as well as a fixed number of registers (independent of the size of the population), each of which can store an element from a totally ordered set S of samples. Whenever two agents interact with each other, they update their states and the values stored in their registers according to a joint transition function. This transition function is also restricted; it only allows (a) comparisons and (b) copy / paste operations for the sample values that are stored in the registers of the two interacting agents.
Agents can only meet in pairs via a fair scheduler and are required to eventually converge to the same output value of the function that the protocol globally and stably computes.
We present two different APPs for stably computing the median of the input values, initially stored on the agents of the population.
Our first APP, in which every agent has 3 registers and no states, stably computes (with probability 1)
the median under any fair scheduler in any strongly connected directed (or connected undirected) interaction graph.
Under the probabilistic scheduler, we show that our protocol stably computes the median in O(n^6) number of interactions in a connected undirected interaction graph of n agents.
Our second APP, in which every agent has 2 registers and O(n^2 log{n}) states, computes to the correct median of the input with high probability in O(n^3 log{n}) interactions, assuming the probabilistic scheduler and the complete interaction graph. Finally we present a third APP which, for any k, stably computes the k-th smallest element of the input of the population under any fair scheduler and in any strongly connected directed (or connected undirected) interaction graph. In this APP every agent has 2 registers and n states. Upon convergence every agent has a different state; all these states provide a total ordering of the agents with respect to their input values.
Cite as
George B. Mertzios, Sotiris E. Nikoletseas, Christoforos L. Raptopoulos, and Paul G. Spirakis. Stably Computing Order Statistics with Arithmetic Population Protocols. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 68:1-68:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{mertzios_et_al:LIPIcs.MFCS.2016.68,
author = {Mertzios, George B. and Nikoletseas, Sotiris E. and Raptopoulos, Christoforos L. and Spirakis, Paul G.},
title = {{Stably Computing Order Statistics with Arithmetic Population Protocols}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {68:1--68:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.68},
URN = {urn:nbn:de:0030-drops-64805},
doi = {10.4230/LIPIcs.MFCS.2016.68},
annote = {Keywords: arithmetic population protocols, order statistics, median, k-minimum element}
}
Document
Shortest Unique Substring Queries on Run-Length Encoded Strings
Abstract
We consider the problem of answering shortest unique substring (SUS) queries on run-length encoded strings. For a string S, a unique substring u = S[i..j] is said to be a shortest unique substring (SUS) of S containing an interval [s, t] (i <= s <= t <= j) if for any i' <= s <= t <= j' with j-i > j'-i', S[i'..j'] occurs at least twice in S.
Given a run-length encoding of size m of a string of length N, we show that we can construct a data structure of size O(m+pi_s(N, m)) in O(m log m + pi_c(N, m)) time such that queries can be answered in
O(pi_q(N, m) + k) time, where k is the size of the output (the number of SUSs), and pi_s(N,m), pi_c(N,m), pi_q(N,m) are, respectively, the size, construction time, and query time for a predecessor/successor query data structure of m elements for the universe of [1,N]. Using the data structure by Beam and Fich (JCSS 2002), this results in a data structure of O(m) space that is constructed in O(m log m) time, and answers queries in O(sqrt(log m/loglog m)+k) time.
Cite as
Takuya Mieno, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Shortest Unique Substring Queries on Run-Length Encoded Strings. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 69:1-69:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{mieno_et_al:LIPIcs.MFCS.2016.69,
author = {Mieno, Takuya and Inenaga, Shunsuke and Bannai, Hideo and Takeda, Masayuki},
title = {{Shortest Unique Substring Queries on Run-Length Encoded Strings}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {69:1--69:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.69},
URN = {urn:nbn:de:0030-drops-65033},
doi = {10.4230/LIPIcs.MFCS.2016.69},
annote = {Keywords: string algorithms, shortest unique substring, run-length encoding}
}
Document
Shattered Sets and the Hilbert Function
Abstract
We study complexity measures on subsets of the boolean hypercube and exhibit connections between algebra (the Hilbert function) and combinatorics (VC theory). These connections yield results in both directions. Our main complexity-theoretic result demonstrates that a large and natural family of linear program feasibility problems cannot be computed by polynomial-sized constant-depth circuits. Moreover, our result applies to a stronger regime in which the hyperplanes are fixed and only the directions of the inequalities are given as input to the circuit. We derive this result by proving that a rich class of extremal functions in VC theory cannot be approximated by low-degree polynomials. We also present applications of algebra to combinatorics. We provide a new algebraic proof of the Sandwich Theorem, which is a generalization of the well-known Sauer-Perles-Shelah Lemma.
Finally, we prove a structural result about downward-closed sets, related to the Chvatal conjecture in extremal combinatorics.
Cite as
Shay Moran and Cyrus Rashtchian. Shattered Sets and the Hilbert Function. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 70:1-70:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{moran_et_al:LIPIcs.MFCS.2016.70,
author = {Moran, Shay and Rashtchian, Cyrus},
title = {{Shattered Sets and the Hilbert Function}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {70:1--70:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.70},
URN = {urn:nbn:de:0030-drops-64814},
doi = {10.4230/LIPIcs.MFCS.2016.70},
annote = {Keywords: VC dimension, shattered sets, sandwich theorem, Hilbert function, polynomial method, linear programming, Chvatal's conjecture, downward-closed sets}
}
Document
Optimal Sparsification for Some Binary CSPs Using Low-Degree Polynomials
Abstract
This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization. Existing results show that if NP is not contained in coNP/poly, no efficient preprocessing algorithm can reduce n-variable instances of CNF-SAT with d literals per clause, to equivalent instances with O(n^{d-epsilon}) bits for any epsilon > 0. For the Not-All-Equal SAT problem, a compression to size tilde-O(n^{d-1}) exists. We put these results in a common framework by analyzing the compressibility of binary CSPs. We characterize constraint types based on the minimum degree of multivariate polynomials whose roots correspond to the satisfying assignments, obtaining (nearly) matching upper and lower bounds in several settings. Our lower bounds show that not just the number of constraints, but also the encoding size of individual constraints plays an important role. For example, for Exact Satisfiability with unbounded clause length it is possible to efficiently reduce the number of constraints to n+1, yet no polynomial-time algorithm can reduce to an equivalent instance with O(n^{2-epsilon}) bits for any epsilon > 0, unless NP is contained in coNP/poly.
Cite as
Bart M. P. Jansen and Astrid Pieterse. Optimal Sparsification for Some Binary CSPs Using Low-Degree Polynomials. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 71:1-71:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{jansen_et_al:LIPIcs.MFCS.2016.71,
author = {Jansen, Bart M. P. and Pieterse, Astrid},
title = {{Optimal Sparsification for Some Binary CSPs Using Low-Degree Polynomials}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {71:1--71:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.71},
URN = {urn:nbn:de:0030-drops-64821},
doi = {10.4230/LIPIcs.MFCS.2016.71},
annote = {Keywords: constraint satisfaction problem, sparsification, satisfiability, kernelization}
}
Document
Fully Dynamic Data Structure for LCE Queries in Compressed Space
Abstract
A Longest Common Extension (LCE) query on a text T of length N asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding G of size w = O(min(z log N log^* M, N)) [Mehlhorn et al., Algorithmica 17(2):183-198, 1997] of T, which can be seen as a compressed representation of T, has a capability to support LCE queries in O(log N + log ell log^* M) time, where ell is the answer to the query, z is the size of the Lempel-Ziv77 (LZ77) factorization of T, and M >= 4N is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, G can be enhanced to support efficient update operations: After processing G in O(w f_A) time, we can insert/delete any (sub)string of length y into/from an arbitrary position of T in O((y + log Nlog^* M) f_A) time, where f_A = O(min{ (loglog M loglog w)/(logloglog M), sqrt(log w/loglog w)}). This yields the first fully dynamic LCE data structure working in compressed space. We also present efficient construction algorithms from various types of inputs: We can construct G in O(N f_A) time from uncompressed string T; in O(n loglog (n log^* M) log N log^* M) time from grammar-compressed string T represented by a straight-line program of size n; and in O(z f_A log N log^* M) time from LZ77-compressed string T with z factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing.
Cite as
Takaaki Nishimoto, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Fully Dynamic Data Structure for LCE Queries in Compressed Space. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 72:1-72:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{nishimoto_et_al:LIPIcs.MFCS.2016.72,
author = {Nishimoto, Takaaki and I, Tomohiro and Inenaga, Shunsuke and Bannai, Hideo and Takeda, Masayuki},
title = {{Fully Dynamic Data Structure for LCE Queries in Compressed Space}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {72:1--72:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.72},
URN = {urn:nbn:de:0030-drops-65045},
doi = {10.4230/LIPIcs.MFCS.2016.72},
annote = {Keywords: dynamic texts, longest common extension (LCE) queries, straight-line program}
}
Document
Undecidability of Two-dimensional Robot Games
Abstract
Robot game is a two-player vector addition game played on the integer lattice Z^n. Both players have sets of vectors and in each turn the vector chosen by a player is added to the current configuration vector of the game. One of the players, called Eve, tries to play the game from the initial configuration to the origin while the other player, Adam, tries to avoid the origin. The problem is to decide whether or not Eve has a winning strategy. In this paper we prove undecidability of the robot game in dimension two answering the question formulated by Doyen and Rabinovich in 2011 and closing the gap between undecidable and decidable cases.
Cite as
Reino Niskanen, Igor Potapov, and Julien Reichert. Undecidability of Two-dimensional Robot Games. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 73:1-73:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{niskanen_et_al:LIPIcs.MFCS.2016.73,
author = {Niskanen, Reino and Potapov, Igor and Reichert, Julien},
title = {{Undecidability of Two-dimensional Robot Games}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {73:1--73:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.73},
URN = {urn:nbn:de:0030-drops-64839},
doi = {10.4230/LIPIcs.MFCS.2016.73},
annote = {Keywords: reachability games, vector addition game, decidability, winning strategy}
}
Document
Algebraic Independence over Positive Characteristic: New Criterion and Applications to Locally Low Algebraic Rank Circuits
Abstract
The motivation for this work comes from two problems--test algebraic independence of arithmetic circuits over a field of small characteristic, and generalize the structural property of algebraic dependence used by (Kumar, Saraf CCC'16) to arbitrary fields.
It is known that in the case of zero, or large characteristic, using a classical criterion based on the Jacobian, we get a randomized poly-time algorithm to test algebraic independence. Over small characteristic, the Jacobian criterion fails and there is no subexponential time algorithm known. This problem could well be conjectured to be in RP, but the current best algorithm puts it in NP^#P (Mittmann, Saxena, Scheiblechner Trans.AMS'14). Currently, even the case of two bivariate circuits over F_2 is open. We come up with a natural generalization of Jacobian criterion, that works over all characteristic. The new criterion is efficient if the underlying inseparable degree is promised to be a constant. This is a modest step towards the open question of fast independence testing, over finite fields, posed in (Dvir, Gabizon, Wigderson FOCS'07).
In a set of linearly dependent polynomials, any polynomial can be written as a linear combination of the polynomials forming a basis. The analogous property for algebraic dependence is false, but a property approximately in that spirit is named as ``functional dependence'' in (Kumar, Saraf CCC'16) and proved for zero or large characteristic. We show that functional dependence holds for arbitrary fields, thereby answering the open questions in (Kumar, Saraf CCC'16). Following them we use the functional dependence lemma to prove the first exponential lower bound for locally low algebraic rank circuits for arbitrary fields (a model that strongly generalizes homogeneous depth-4 circuits). We also recover their quasipoly-time hitting-set for such models, for fields of characteristic smaller than the ones known before.
Our results show that approximate functional dependence is indeed a more fundamental concept than the Jacobian as it is field independent. We achieve the former by first picking a ``good'' transcendence basis, then translating the circuits by new variables, and finally approximating them by truncating higher degree monomials. We give a tight analysis of the ``degree'' of approximation needed in the criterion. To get the locally low algebraic rank circuit applications we follow the known shifted partial derivative based methods.
Cite as
Anurag Pandey, Nitin Saxena, and Amit Sinhababu. Algebraic Independence over Positive Characteristic: New Criterion and Applications to Locally Low Algebraic Rank Circuits. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 74:1-74:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{pandey_et_al:LIPIcs.MFCS.2016.74,
author = {Pandey, Anurag and Saxena, Nitin and Sinhababu, Amit},
title = {{Algebraic Independence over Positive Characteristic: New Criterion and Applications to Locally Low Algebraic Rank Circuits}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {74:1--74:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.74},
URN = {urn:nbn:de:0030-drops-65057},
doi = {10.4230/LIPIcs.MFCS.2016.74},
annote = {Keywords: independence, transcendence, finite field, Hasse-Schmidt, Jacobian, differential, inseparable, circuit, identity testing, lower bound, depth-4, shifte}
}
Document
Parameterized Algorithms on Perfect Graphs for Deletion to (r,l)-Graphs
Abstract
For fixed integers r,l >= 0, a graph G is called an (r,l)-graph if the vertex set V(G) can be partitioned into r independent sets and l cliques. Such a graph is also said to have cochromatic number r+l. The class of (r,l) graphs generalizes r-colourable graphs (when l=0) and hence not surprisingly, determining whether a given graph is an (r,l)-graph is NP-hard even when r >= 3 or l >= 3 in general graphs.
When r and ell are part of the input, then the recognition problem is NP-hard even if the input graph is a perfect graph (where the Chromatic Number problem is solvable in polynomial time). It is also known to be fixed-parameter tractable (FPT) on perfect graphs when parameterized by r and l. I.e. there is an f(r+l) n^O(1) algorithm on perfect graphs on n vertices where f is a function of r and l. Observe that such an algorithm is unlikely on general graphs as the problem is NP-hard even for constant r and l.
In this paper, we consider the parameterized complexity of the following problem, which we call Vertex Partization. Given a perfect graph G and positive integers r,l,k decide whether there exists a set S subset or equal to V(G) of size at most k such that the deletion of S from G results in an (r,l)-graph. This problem generalizes well studied problems such as Vertex Cover (when r=1 and l=0), Odd Cycle Transversal (when r=2, l=0) and Split Vertex Deletion (when r=1=l).
1. Vertex Partization on perfect graphs is FPT when parameterized by k+r+l.
2. The problem, when parameterized by k+r+l, does not admit any polynomial sized kernel, under standard complexity theoretic assumptions. In other words, in polynomial time, the input graph cannot be compressed to an equivalent instance of size polynomial in k+r+l. In fact, our result holds even when k=0.
3. When r,ell are universal constants, then Vertex Partization on perfect graphs, parameterized by k, has a polynomial sized kernel.
Cite as
Sudeshna Kolay, Fahad Panolan, Venkatesh Raman, and Saket Saurabh. Parameterized Algorithms on Perfect Graphs for Deletion to (r,l)-Graphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 75:1-75:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{kolay_et_al:LIPIcs.MFCS.2016.75,
author = {Kolay, Sudeshna and Panolan, Fahad and Raman, Venkatesh and Saurabh, Saket},
title = {{Parameterized Algorithms on Perfect Graphs for Deletion to (r,l)-Graphs}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {75:1--75:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.75},
URN = {urn:nbn:de:0030-drops-64846},
doi = {10.4230/LIPIcs.MFCS.2016.75},
annote = {Keywords: graph deletion, FPT algorithms, polynomial kernels}
}
Document
Supplementarity is Necessary for Quantum Diagram Reasoning
Abstract
The ZX-calculus is a powerful diagrammatic language for quantum mechanics and quantum information processing. We prove that its pi/4-fragment is not complete, in other words the ZX-calculus is not complete for the so called "Clifford+T quantum mechanics". The completeness of this fragment was one of the main open problems in categorical quantum mechanics, a programme initiated by Abramsky and Coecke. The ZX-calculus was known to be incomplete for quantum mechanics. On the other hand, its pi/2-fragment is known to be complete, i.e. the ZX-calculus is complete for the so called "stabilizer quantum mechanics". Deciding whether its pi/4-fragment is complete is a crucial step in the development of the ZX-calculus since this fragment is approximately universal for quantum mechanics, contrary to the pi/2-fragment.
To establish our incompleteness result, we consider a fairly simple property of quantum states called supplementarity. We show that supplementarity can be derived in the ZX-calculus if and only if the angles involved in this equation are multiples of pi/2. In particular, the impossibility to derive supplementarity for pi/4 implies the incompleteness of the ZX-calculus for Clifford+T quantum mechanics. As a consequence, we propose to add the supplementarity to the set of rules of the ZX-calculus.
We also show that if a ZX-diagram involves antiphase twins, they can be merged when the ZX-calculus is augmented with the supplementarity rule. Merging antiphase twins makes diagrammatic reasoning much easier and provides a purely graphical meaning to the supplementarity rule.
Cite as
Simon Perdrix and Quanlong Wang. Supplementarity is Necessary for Quantum Diagram Reasoning. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 76:1-76:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{perdrix_et_al:LIPIcs.MFCS.2016.76,
author = {Perdrix, Simon and Wang, Quanlong},
title = {{Supplementarity is Necessary for Quantum Diagram Reasoning}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {76:1--76:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.76},
URN = {urn:nbn:de:0030-drops-65062},
doi = {10.4230/LIPIcs.MFCS.2016.76},
annote = {Keywords: quantum diagram reasoning, completeness, ZX-calculus, quantum computing, categorical quantum mechanics}
}
Document
The Covering Problem: A Unified Approach for Investigating the Expressive Power of Logics
Abstract
An important endeavor in computer science is to precisely understand the expressive power of logical formalisms over discrete structures, such as words. Naturally, "understanding" is not a mathematical notion. Therefore, this investigation requires a concrete objective to capture such a notion. In the literature, the standard choice for this objective is the membership problem, whose aim is to find a procedure deciding whether an input regular language can be defined in the logic under study. This approach was cemented as the "right" one by the seminal work of Schuetzenberger, McNaughton and Papert on first-order logic and has been in use since then.
However, membership questions are hard: for several important fragments, researchers have failed in this endeavor despite decades of investigation. In view of recent results on one of the most famous open questions, namely the quantifier alternation hierarchy of first-order logic, an explanation may be that membership is too restrictive as a setting. These new results were indeed obtained by considering more general problems than membership, taking advantage of the increased flexibility of the enriched mathematical setting. This opens a promising avenue of research and efforts have been devoted at identifying and solving such problems for natural fragments. However, until now, these problems have been ad hoc, most fragments relying on a specific one. A unique new problem replacing membership as the right one is still missing.
The main contribution of this paper is a suitable candidate to play this role: the Covering Problem. We motivate this problem with three arguments. First, it admits an elementary set theoretic formulation, similar to membership. Second, we are able to reexplain or generalize all known results with this problem. Third, we develop a mathematical framework as well as a methodology tailored to the investigation of this problem.
Cite as
Thomas Place and Marc Zeitoun. The Covering Problem: A Unified Approach for Investigating the Expressive Power of Logics. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 77:1-77:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{place_et_al:LIPIcs.MFCS.2016.77,
author = {Place, Thomas and Zeitoun, Marc},
title = {{The Covering Problem: A Unified Approach for Investigating the Expressive Power of Logics}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {77:1--77:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.77},
URN = {urn:nbn:de:0030-drops-64857},
doi = {10.4230/LIPIcs.MFCS.2016.77},
annote = {Keywords: membership problem, separation problem, covering problem, regular languages, logics, decidable characterizations}
}
Document
On the Complexity of Branching Games with Regular Conditions
Abstract
Infinite duration games with regular conditions are one of the crucial tools in the areas of verification and synthesis. In this paper we consider a branching variant of such games - the game contains branching vertices that split the play into two independent sub-games. Thus, a play has the form of~an~infinite tree. The winner of the play is determined by a winning condition specified as a set of infinite trees. Games of this kind were used by Mio to provide a game semantics for the probabilistic mu-calculus. He used winning conditions defined in terms of parity games on trees. In this work we consider a more general class of winning conditions, namely those definable by finite automata on infinite trees. Our games can be seen as a branching-time variant of the stochastic games on graphs.
We address the question of determinacy of a branching game and the problem of computing the optimal game value for each of the players. We consider both the stochastic and non-stochastic variants of the games. The questions under consideration are parametrised by the family of strategies we allow: either mixed, behavioural, or pure.
We prove that in general, branching games are not determined under mixed strategies. This holds even for topologically simple winning conditions (differences of two open sets) and non-stochastic arenas. Nevertheless, we show that the games become determined under mixed strategies if we restrict the winning conditions to open sets of trees. We prove that the problem of comparing the game value to a rational threshold is undecidable for branching games with regular conditions in all non-trivial stochastic cases. In the non-stochastic cases we provide exact bounds on the complexity of the problem. The only case left open is the 0-player stochastic case, i.e. the problem of computing the measure of a given regular language of infinite trees.
Cite as
Marcin Przybylko and Michal Skrzypczak. On the Complexity of Branching Games with Regular Conditions. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 78:1-78:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{przybylko_et_al:LIPIcs.MFCS.2016.78,
author = {Przybylko, Marcin and Skrzypczak, Michal},
title = {{On the Complexity of Branching Games with Regular Conditions}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {78:1--78:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.78},
URN = {urn:nbn:de:0030-drops-64865},
doi = {10.4230/LIPIcs.MFCS.2016.78},
annote = {Keywords: stochastic games, meta-parity games, infinite trees, regular languages, parity automata}
}
Document
Symbolic Lookaheads for Bottom-up Parsing
Abstract
We present algorithms for the construction of LALR(1) parsing tables, and of LR(1) parsing tables of reduced size. We first define specialized characteristic automata whose states are parametric w.r.t. variables symbolically representing lookahead-sets. The propagation flow of lookaheads is kept in the form of a system of recursive equations, which is resolved to obtain the concrete LALR(1) table. By inspection of the LALR(1) automaton and of its lookahead ropagation flow, we decide whether the grammar is LR(1) or not. In the positive case, an LR(1) parsing table of reduced size is computed by refinement of the LALR(1) table.
Cite as
Paola Quaglia. Symbolic Lookaheads for Bottom-up Parsing. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{quaglia:LIPIcs.MFCS.2016.79,
author = {Quaglia, Paola},
title = {{Symbolic Lookaheads for Bottom-up Parsing}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {79:1--79:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.79},
URN = {urn:nbn:de:0030-drops-64876},
doi = {10.4230/LIPIcs.MFCS.2016.79},
annote = {Keywords: LALR(1) grammars; LR(1) grammars; bottom-up parsing}
}
Document
Structural Control in Weighted Voting Games
Abstract
Inspired by the study of control scenarios in elections and complementing manipulation and bribery settings in cooperative games with transferable utility, we introduce the notion of structural control in weighted voting games. We model two types of influence, adding players to and deleting players from a game, with goals such as increasing a given player's Shapley-Shubik or probabilistic Penrose-Banzhaf index in relation to the original game. We study the computational complexity of the problems of whether such structural changes can achieve the desired effect.
Cite as
Anja Rey and Jörg Rothe. Structural Control in Weighted Voting Games. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 80:1-80:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{rey_et_al:LIPIcs.MFCS.2016.80,
author = {Rey, Anja and Rothe, J\"{o}rg},
title = {{Structural Control in Weighted Voting Games}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {80:1--80:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.80},
URN = {urn:nbn:de:0030-drops-64883},
doi = {10.4230/LIPIcs.MFCS.2016.80},
annote = {Keywords: algorithmic games theory, weighted voting games, structural control, power indices, computational complexity}
}
Document
Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable
Abstract
We show that every binary pattern of length greater than 14 is abelian-2-avoidable. The best known upper bound on the length of abelian-2-unavoidable binary pattern was 118, and the best known lower bound is 7.
We designed an algorithm to decide, under some reasonable assumptions, if a morphic word avoids a pattern in the abelian sense. This algorithm is then used to show that some binary patterns are abelian-2-avoidable. We finally use this list of abelian-2-avoidable pattern to show our result. We also discuss the avoidability of binary patterns on 3 and 4 letters.
Cite as
Matthieu Rosenfeld. Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 81:1-81:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{rosenfeld:LIPIcs.MFCS.2016.81,
author = {Rosenfeld, Matthieu},
title = {{Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {81:1--81:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.81},
URN = {urn:nbn:de:0030-drops-64892},
doi = {10.4230/LIPIcs.MFCS.2016.81},
annote = {Keywords: combinatorics on words, pattern avoidance, abelian repetitions}
}
Document
Bounded Depth Circuits with Weighted Symmetric Gates: Satisfiability, Lower Bounds and Compression
Abstract
A Boolean function f:{0,1}^n -> {0,1} is weighted symmetric if there exist a function g: Z -> {0,1} and integers w_0, w_1, ..., w_n such that f(x_1, ...,x_n) = g(w_0+sum_{i=1}^n w_i x_i) holds.
In this paper, we present algorithms for the circuit satisfiability problem of bounded depth circuits with AND, OR, NOT gates and a limited number of weighted symmetric gates. Our algorithms run in time super-polynomially faster than 2^n even when the number of gates is super-polynomial and the maximum weight of symmetric gates is nearly exponential. With an additional trick, we give an algorithm for the maximum satisfiability problem that runs in time poly(n^t)*2^{n-n^{1/O(t)}} for instances with n variables, O(n^t) clauses and arbitrary weights. To the best of our knowledge, this is the first moderately exponential time algorithm even for Max 2SAT instances with arbitrary weights.
Through the analysis of our algorithms, we obtain average-case lower bounds and compression algorithms for such circuits and worst-case lower bounds for majority votes of such circuits, where all the lower bounds are against the generalized Andreev function. Our average-case lower bounds might be of independent interest in the sense that previous ones for similar circuits with arbitrary symmetric gates rely on communication complexity lower bounds while ours are based on the restriction method.
Cite as
Takayuki Sakai, Kazuhisa Seto, Suguru Tamaki, and Junichi Teruyama. Bounded Depth Circuits with Weighted Symmetric Gates: Satisfiability, Lower Bounds and Compression. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 82:1-82:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{sakai_et_al:LIPIcs.MFCS.2016.82,
author = {Sakai, Takayuki and Seto, Kazuhisa and Tamaki, Suguru and Teruyama, Junichi},
title = {{Bounded Depth Circuits with Weighted Symmetric Gates: Satisfiability, Lower Bounds and Compression}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {82:1--82:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.82},
URN = {urn:nbn:de:0030-drops-64905},
doi = {10.4230/LIPIcs.MFCS.2016.82},
annote = {Keywords: exponential time algorithm, circuit complexity, circuit minimization, maximum satisfiability}
}
Document
Transducer-Based Rewriting Games for Active XML
Abstract
Context-free games are two-player rewriting games that are played on nested strings representing XML documents with embedded function symbols. These games were introduced to model rewriting processes for intensional documents in the Active XML framework, where input documents are to be rewritten into a given target schema by calls to external services.
This paper studies the setting where dependencies between inputs and outputs of service calls are modelled by transducers, which has not been examined previously. It defines transducer models operating on nested words and studies their properties, as well as the computational complexity of the winning problem for transducer-based context-free games in several scenarios. While the complexity of this problem is quite high in most settings (ranging from NP-complete to undecidable), some tractable restrictions are also identified.
Cite as
Martin Schuster. Transducer-Based Rewriting Games for Active XML. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 83:1-83:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{schuster:LIPIcs.MFCS.2016.83,
author = {Schuster, Martin},
title = {{Transducer-Based Rewriting Games for Active XML}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {83:1--83:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.83},
URN = {urn:nbn:de:0030-drops-64910},
doi = {10.4230/LIPIcs.MFCS.2016.83},
annote = {Keywords: active XML, computational complexity, nested words, transducers, rewriting games}
}
Document
Vector Reachability Problem in SL(2, Z)
Abstract
The decision problems on matrices were intensively studied for many decades as matrix products play an essential role in the representation of various computational processes. However, many computational problems for matrix semigroups are inherently difficult to solve even for problems in low dimensions and most matrix semigroup problems become undecidable in general starting from dimension three or four.
This paper solves two open problems about the decidability of the vector reachability problem over a finitely generated semigroup of matrices from SL(2, Z) and the point to point reachability (over rational numbers) for fractional linear transformations, where associated matrices are from SL(2, Z). The approach to solving reachability problems is based on the characterization of reachability paths between points which is followed by the translation of numerical problems on matrices into computational and combinatorial problems on words and formal languages. We also give a geometric interpretation of reachability paths and extend the decidability results to matrix products represented by arbitrary labelled directed graphs. Finally, we will use this technique to prove that a special case of the scalar reachability problem is decidable.
Cite as
Igor Potapov and Pavel Semukhin. Vector Reachability Problem in SL(2, Z). In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 84:1-84:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{potapov_et_al:LIPIcs.MFCS.2016.84,
author = {Potapov, Igor and Semukhin, Pavel},
title = {{Vector Reachability Problem in SL(2, Z)}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {84:1--84:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.84},
URN = {urn:nbn:de:0030-drops-64925},
doi = {10.4230/LIPIcs.MFCS.2016.84},
annote = {Keywords: matrix semigroup, vector reachability problem, special linear group, linear fractional transformation, automata and formal languages}
}
Document
The Generalised Colouring Numbers on Classes of Bounded Expansion
Abstract
The generalised colouring numbers adm_r(G), col_r(G), and wcol_r(G) were introduced by Kierstead and Yang as generalisations of the usual colouring number, also known as the degeneracy of a graph, and have since then found important applications in the theory of bounded expansion and nowhere dense classes of graphs, introduced by Nesetril and Ossona de Mendez. In this paper, we study the relation of the colouring numbers with two other measures that characterise nowhere dense classes of graphs, namely with uniform quasi-wideness, studied first by Dawar et al. in the context of preservation theorems for first-order logic, and with the splitter game, introduced by Grohe et al. We show that every graph excluding a fixed topological minor admits a universal order, that is, one order witnessing that the colouring numbers are small for every value of r. Finally, we use our construction of such orders to give a new proof of a result of Eickmeyer and Kawarabayashi, showing that the model-checking problem for successor-invariant first-order formulas is fixed parameter tractable on classes of graphs with excluded topological minors.
Cite as
Stephan Kreutzer, Michal Pilipczuk, Roman Rabinovich, and Sebastian Siebertz. The Generalised Colouring Numbers on Classes of Bounded Expansion. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 85:1-85:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{kreutzer_et_al:LIPIcs.MFCS.2016.85,
author = {Kreutzer, Stephan and Pilipczuk, Michal and Rabinovich, Roman and Siebertz, Sebastian},
title = {{The Generalised Colouring Numbers on Classes of Bounded Expansion}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {85:1--85:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.85},
URN = {urn:nbn:de:0030-drops-64937},
doi = {10.4230/LIPIcs.MFCS.2016.85},
annote = {Keywords: graph structure theory, nowhere dense graphs, generalised colouring numbers, splitter game, first-order model-checking}
}
Document
Polynomial Space Randomness in Analysis
Abstract
We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko's framework for polynomial space computability in R^n to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem characterizes weakly pspace random points. That is, a point x is weakly pspace random if and only if the Lebesgue differentiation theorem holds for a point x for every pspace L_1-computable function.
Cite as
Xiang Huang and Donald M. Stull. Polynomial Space Randomness in Analysis. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 86:1-86:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{huang_et_al:LIPIcs.MFCS.2016.86,
author = {Huang, Xiang and Stull, Donald M.},
title = {{Polynomial Space Randomness in Analysis}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {86:1--86:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.86},
URN = {urn:nbn:de:0030-drops-64943},
doi = {10.4230/LIPIcs.MFCS.2016.86},
annote = {Keywords: algorithmic randomness, computable analysis, resource-bounded randomness, complexity theory}
}
Document
Finding a Maximum 2-Matching Excluding Prescribed Cycles in Bipartite Graphs
Abstract
We introduce a new framework of restricted 2-matchings close to Hamilton cycles. For an undirected graph (V,E) and a family U of vertex subsets, a 2-matching F is called U-feasible if, for each setU in U, F contains at most |setU|-1 edges in the subgraph induced by U. Our framework includes C_{<=k}-free 2-matchings, i.e., 2-matchings without cycles of at most k edges, and 2-factors covering prescribed edge cuts, both of which are intensively studied as relaxations of Hamilton cycles. The problem of finding a maximum U-feasible 2-matching is NP-hard. We prove that the problem is tractable when the graph is bipartite and each setU in U induces a Hamilton-laceable graph. This case generalizes the C_{<=4}-free 2-matching problem in bipartite graphs. We establish a min-max theorem, a combinatorial polynomial-time algorithm, and decomposition theorems by extending the theory of C_{<=4}-free 2-matchings. Our result provides the first polynomially solvable case for the maximum C_{<=k}-free 2-matching problem for k >= 5. For instance, in bipartite graphs in which every cycle of length six has at least two chords, our algorithm solves the maximum C_{<=6}-free 2-matching problem in O(n^2 m) time, where n and m are the numbers of vertices and edges, respectively.
Cite as
Kenjiro Takazawa. Finding a Maximum 2-Matching Excluding Prescribed Cycles in Bipartite Graphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 87:1-87:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{takazawa:LIPIcs.MFCS.2016.87,
author = {Takazawa, Kenjiro},
title = {{Finding a Maximum 2-Matching Excluding Prescribed Cycles in Bipartite Graphs}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {87:1--87:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.87},
URN = {urn:nbn:de:0030-drops-64950},
doi = {10.4230/LIPIcs.MFCS.2016.87},
annote = {Keywords: optimization algorithms, matching theory, traveling salesman problem, restricted 2-matchings, Hamilton-laceable graphs}
}
Document
Transformation Between Regular Expressions and omega-Automata
Abstract
We propose a new definition of regular expressions for describing languages of omega-words, called infinity-regular expressions. These expressions are obtained by adding to the standard regular expression on finite words an operator infinity that acts similar to the Kleene-star but can be iterated finitely or infinitely often (as opposed to the omega-operator from standard omega-regular expressions, which has to be iterated infinitely often). We show that standard constructions between automata and regular expressions for finite words can smoothly be adapted to infinite words in this setting: We extend the Glushkov construction yielding a simple translation of infinity-regular expressions into parity automata, and we show how to translate parity automata into infinity-regular expressions by the classical state elimination technique, where in both cases the nesting of the * and the infinity operators corresponds to the priority range used in the parity automaton. We also briefly discuss the concept of deterministic expressions that directly transfers from standard regular expressions to infinity-regular expressions.
Cite as
Christof Löding and Andreas Tollkötter. Transformation Between Regular Expressions and omega-Automata. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 88:1-88:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{loding_et_al:LIPIcs.MFCS.2016.88,
author = {L\"{o}ding, Christof and Tollk\"{o}tter, Andreas},
title = {{Transformation Between Regular Expressions and omega-Automata}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {88:1--88:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.88},
URN = {urn:nbn:de:0030-drops-64962},
doi = {10.4230/LIPIcs.MFCS.2016.88},
annote = {Keywords: infinity regular expressions, parity automata}
}
Document
An Improved Approximation Algorithm for the Traveling Tournament Problem with Maximum Trip Length Two
Abstract
The Traveling Tournament Problem is a complex combinatorial optimization problem in tournament timetabling, which asks a schedule of home/away games meeting specific feasibility requirements, while also minimizing the total distance traveled by all the n teams (n is even). Despite intensive algorithmic research on this problem over the last decade, most instances with more than 10 teams in well-known benchmarks are still unsolved. In this paper, we give a practical approximation algorithm for the problem with constraints such that at most two consecutive home games or away games are allowed. Our algorithm, that generates feasible schedules based on minimum perfect matchings in the underlying graph, not only improves the previous approximation ratio from (1+16/n) to about (1+4/n) but also has very good experimental performances. By applying our schedules on known benchmark sets, we can beat all previously-known results of instances with n being a multiple of 4 by 3% to 10%.
Cite as
Mingyu Xiao and Shaowei Kou. An Improved Approximation Algorithm for the Traveling Tournament Problem with Maximum Trip Length Two. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 89:1-89:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
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@InProceedings{xiao_et_al:LIPIcs.MFCS.2016.89,
author = {Xiao, Mingyu and Kou, Shaowei},
title = {{An Improved Approximation Algorithm for the Traveling Tournament Problem with Maximum Trip Length Two}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {89:1--89:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.89},
URN = {urn:nbn:de:0030-drops-64976},
doi = {10.4230/LIPIcs.MFCS.2016.89},
annote = {Keywords: sports scheduling, traveling tournament problem, approximation algorithms, timetabling combinatorial optimization}
}