Volume
LIPIcs, Volume 126
36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
Event
STACS 2019, March 13-16, 2019, Berlin, GermanyEditors
Publication Details
- published at: 2019-03-12
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-100-9
- DBLP: db/conf/stacs/stacs2019
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Document
Complete Volume
LIPIcs, Volume 126, STACS'19, Complete Volume
Abstract
LIPIcs, Volume 126, STACS'19, Complete Volume
Cite as
36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@Proceedings{niedermeier_et_al:LIPIcs.STACS.2019,
title = {{LIPIcs, Volume 126, STACS'19, Complete Volume}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019},
URN = {urn:nbn:de:0030-drops-103324},
doi = {10.4230/LIPIcs.STACS.2019},
annote = {Keywords: Theory of computation, Models of computation, Mathematics of computing, Combinatorics, Graph theory, Formal language theory, Logic}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{niedermeier_et_al:LIPIcs.STACS.2019.0,
author = {Niedermeier, Rolf and Paul, Christophe},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {0:i--0:xvi},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.0},
URN = {urn:nbn:de:0030-drops-102392},
doi = {10.4230/LIPIcs.STACS.2019.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
Computational Complexity and Partition Functions (Invited Talk)
Abstract
This paper is an extended abstract of my STACS 2019 talk "Computational Complexity and Partition Functions".
Cite as
Leslie Ann Goldberg. Computational Complexity and Partition Functions (Invited Talk). In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 1:1-1:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{goldberg:LIPIcs.STACS.2019.1,
author = {Goldberg, Leslie Ann},
title = {{Computational Complexity and Partition Functions}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {1:1--1:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.1},
URN = {urn:nbn:de:0030-drops-102405},
doi = {10.4230/LIPIcs.STACS.2019.1},
annote = {Keywords: partition functions, approximation}
}
Document
Invited Talk
The Many Facets of String Transducers (Invited Talk)
Abstract
Regular word transductions extend the robust notion of regular languages from a qualitative to a quantitative reasoning. They were already considered in early papers of formal language theory, but turned out to be much more challenging. The last decade brought considerable research around various transducer models, aiming to achieve similar robustness as for automata and languages. In this paper we survey some older and more recent results on string transducers. We present classical connections between automata, logic and algebra extended to transducers, some genuine definability questions, and review approaches to the equivalence problem.
Cite as
Anca Muscholl and Gabriele Puppis. The Many Facets of String Transducers (Invited Talk). In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{muscholl_et_al:LIPIcs.STACS.2019.2,
author = {Muscholl, Anca and Puppis, Gabriele},
title = {{The Many Facets of String Transducers}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {2:1--2:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.2},
URN = {urn:nbn:de:0030-drops-102410},
doi = {10.4230/LIPIcs.STACS.2019.2},
annote = {Keywords: String transducers, complexity}
}
Document
Invited Talk
Algorithmic Data Science (Invited Talk)
Abstract
The area of algorithmic data science provides new opportunities for researchers in the algorithmic community. In this paper we will see examples that demonstrate that algorithm engineering is the perfect basis for algorithmic data science. But there are also many open interesting questions for purely theoretically interested computer scientists. In my opinion, these opportunities should be taken because this will be fruitful for both areas, algorithmics as well as data sciences. I like to call for more participation in algorithmic data science by our community. Now we have the opportunity to shape this new emerging field.
Cite as
Petra Mutzel. Algorithmic Data Science (Invited Talk). In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{mutzel:LIPIcs.STACS.2019.3,
author = {Mutzel, Petra},
title = {{Algorithmic Data Science}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {3:1--3:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.3},
URN = {urn:nbn:de:0030-drops-102425},
doi = {10.4230/LIPIcs.STACS.2019.3},
annote = {Keywords: Algorithmic Data Science, Graph Similarity, Weisfeiler-Leman}
}
Document
Tutorial
Fine-Grained Complexity Theory (Tutorial)
Abstract
Suppose the fastest algorithm that we can design for some problem runs in time O(n^2). However, we want to solve the problem on big data inputs, for which quadratic time is impractically slow. We can keep searching for a faster algorithm, but maybe none exists. Is there any reasoning that provides evidence against significantly faster algorithms, and thus allows us to stop searching? In other words, is there an analogue of NP-hardness for polynomial-time problems?
In this tutorial, we will give an introduction to fine-grained complexity theory, which allows to rule out faster algorithms by proving conditional lower bounds via fine-grained reductions from certain key conjectures. We will define these terms and show exemplary lower bounds.
Cite as
Karl Bringmann. Fine-Grained Complexity Theory (Tutorial). In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 4:1-4:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{bringmann:LIPIcs.STACS.2019.4,
author = {Bringmann, Karl},
title = {{Fine-Grained Complexity Theory}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {4:1--4:7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.4},
URN = {urn:nbn:de:0030-drops-102437},
doi = {10.4230/LIPIcs.STACS.2019.4},
annote = {Keywords: Hardness in P, conditional lower bound, fine-grained reduction}
}
Document
Tutorial
From Graph Theory to Network Science: The Natural Emergence of Hyperbolicity (Tutorial)
Abstract
Network science is driven by the question which properties large real-world networks have and how we can exploit them algorithmically. In the past few years, hyperbolic graphs have emerged as a very promising model for scale-free networks. The connection between hyperbolic geometry and complex networks gives insights in both directions:
(1) Hyperbolic geometry forms the basis of a natural and explanatory model for real-world networks. Hyperbolic random graphs are obtained by choosing random points in the hyperbolic plane and connecting pairs of points that are geometrically close. The resulting networks share many structural properties for example with online social networks like Facebook or Twitter. They are thus well suited for algorithmic analyses in a more realistic setting.
(2) Starting with a real-world network, hyperbolic geometry is well-suited for metric embeddings. The vertices of a network can be mapped to points in this geometry, such that geometric distances are similar to graph distances. Such embeddings have a variety of algorithmic applications ranging from approximations based on efficient geometric algorithms to greedy routing solely using hyperbolic coordinates for navigation decisions.
Cite as
Tobias Friedrich. From Graph Theory to Network Science: The Natural Emergence of Hyperbolicity (Tutorial). In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 5:1-5:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{friedrich:LIPIcs.STACS.2019.5,
author = {Friedrich, Tobias},
title = {{From Graph Theory to Network Science: The Natural Emergence of Hyperbolicity}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {5:1--5:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.5},
URN = {urn:nbn:de:0030-drops-102445},
doi = {10.4230/LIPIcs.STACS.2019.5},
annote = {Keywords: Graph Theory, Graph Algorithms, Network Science, Hyperbolic Geometry}
}
Document
The Semialgebraic Orbit Problem
Abstract
The Semialgebraic Orbit Problem is a fundamental reachability question that arises in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurrence sequences, and linear while loops. An instance of the problem comprises a dimension d in N, a square matrix A in Q^{d x d}, and semialgebraic source and target sets S,T subseteq R^d. The question is whether there exists x in S and n in N such that A^nx in T.
The main result of this paper is that the Semialgebraic Orbit Problem is decidable for dimension d <= 3. Our decision procedure relies on separation bounds for algebraic numbers as well as a classical result of transcendental number theory - Baker’s theorem on linear forms in logarithms of algebraic numbers. We moreover argue that our main result represents a natural limit to what can be decided (with respect to reachability) about the orbit of a single matrix. On the one hand, semialgebraic sets are arguably the largest general class of subsets of R^d for which membership is decidable. On the other hand, previous work has shown that in dimension d=4, giving a decision procedure for the special case of the Orbit Problem with singleton source set S and polytope target set T would entail major breakthroughs in Diophantine approximation.
Cite as
Shaull Almagor, Joël Ouaknine, and James Worrell. The Semialgebraic Orbit Problem. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{almagor_et_al:LIPIcs.STACS.2019.6,
author = {Almagor, Shaull and Ouaknine, Jo\"{e}l and Worrell, James},
title = {{The Semialgebraic Orbit Problem}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {6:1--6:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.6},
URN = {urn:nbn:de:0030-drops-102450},
doi = {10.4230/LIPIcs.STACS.2019.6},
annote = {Keywords: linear dynamical systems, Orbit Problem, first order theory of the reals}
}
Document
Best-Of-Two-Worlds Analysis of Online Search
Abstract
In search problems, a mobile searcher seeks to locate a target that hides in some unknown position of the environment. Such problems are typically considered to be of an on-line nature, in that the input is unknown to the searcher, and the performance of a search strategy is usually analyzed by means of the standard framework of the competitive ratio, which compares the cost incurred by the searcher to an optimal strategy that knows the location of the target. However, one can argue that even for simple search problems, competitive analysis fails to distinguish between strategies which, intuitively, should have different performance in practice.
Motivated by the above, in this work we introduce and study measures supplementary to competitive analysis in the context of search problems. In particular, we focus on the well-known problem of linear search, informally known as the cow-path problem, for which there is an infinite number of strategies that achieve an optimal competitive ratio equal to 9. We propose a measure that reflects the rate at which the line is being explored by the searcher, and which can be seen as an extension of the bijective ratio over an uncountable set of requests. Using this measure we show that a natural strategy that explores the line aggressively is optimal among all 9-competitive strategies. This provides, in particular, a strict separation from the competitively optimal doubling strategy, which is much more conservative in terms of exploration. We also provide evidence that this aggressiveness is requisite for optimality, by showing that any optimal strategy must mimic the aggressive strategy in its first few explorations.
Cite as
Spyros Angelopoulos, Christoph Dürr, and Shendan Jin. Best-Of-Two-Worlds Analysis of Online Search. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{angelopoulos_et_al:LIPIcs.STACS.2019.7,
author = {Angelopoulos, Spyros and D\"{u}rr, Christoph and Jin, Shendan},
title = {{Best-Of-Two-Worlds Analysis of Online Search}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {7:1--7:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.7},
URN = {urn:nbn:de:0030-drops-102467},
doi = {10.4230/LIPIcs.STACS.2019.7},
annote = {Keywords: Online computation, search problems, linear search, performance measures}
}
Document
Bipartite Diameter and Other Measures Under Translation
Abstract
Let A and B be two sets of points in R^d, where |A|=|B|=n and the distance between them is defined by some bipartite measure dist(A, B). We study several problems in which the goal is to translate the set B, so that dist(A, B) is minimized. The main measures that we consider are (i) the diameter in two and three dimensions, that is diam(A,B) = max {d(a,b) | a in A, b in B}, where d(a,b) is the Euclidean distance between a and b, (ii) the uniformity in the plane, that is uni(A,B) = diam(A,B) - d(A,B), where d(A,B)=min{d(a,b) | a in A, b in B}, and (iii) the union width in two and three dimensions, that is union_width(A,B) = width(A cup B). For each of these measures we present efficient algorithms for finding a translation of B that minimizes the distance: For diameter we present near-linear-time algorithms in R^2 and R^3, for uniformity we describe a roughly O(n^{9/4})-time algorithm, and for union width we offer a near-linear-time algorithm in R^2 and a quadratic-time one in R^3.
Cite as
Boris Aronov, Omrit Filtser, Matthew J. Katz, and Khadijeh Sheikhan. Bipartite Diameter and Other Measures Under Translation. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{aronov_et_al:LIPIcs.STACS.2019.8,
author = {Aronov, Boris and Filtser, Omrit and Katz, Matthew J. and Sheikhan, Khadijeh},
title = {{Bipartite Diameter and Other Measures Under Translation}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {8:1--8:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.8},
URN = {urn:nbn:de:0030-drops-102476},
doi = {10.4230/LIPIcs.STACS.2019.8},
annote = {Keywords: Translation-invariant similarity measures, Geometric optimization, Minimum-width annulus}
}
Document
Solving Simple Stochastic Games with Few Random Nodes Faster Using Bland’s Rule
Abstract
The best algorithm so far for solving Simple Stochastic Games is Ludwig’s randomized algorithm [Ludwig, 1995] which works in expected 2^{O(sqrt{n})} time. We first give a simpler iterative variant of this algorithm, using Bland’s rule from the simplex algorithm, which uses exponentially less random bits than Ludwig’s version. Then, we show how to adapt this method to the algorithm of Gimbert and Horn [Gimbert and Horn, 2008] whose worst case complexity is O(k!), where k is the number of random nodes. Our algorithm has an expected running time of 2^{O(k)}, and works for general random nodes with arbitrary outdegree and probability distribution on outgoing arcs.
Cite as
David Auger, Pierre Coucheney, and Yann Strozecki. Solving Simple Stochastic Games with Few Random Nodes Faster Using Bland’s Rule. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{auger_et_al:LIPIcs.STACS.2019.9,
author = {Auger, David and Coucheney, Pierre and Strozecki, Yann},
title = {{Solving Simple Stochastic Games with Few Random Nodes Faster Using Bland’s Rule}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {9:1--9:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.9},
URN = {urn:nbn:de:0030-drops-102488},
doi = {10.4230/LIPIcs.STACS.2019.9},
annote = {Keywords: simple stochastic games, randomized algorithm, parametrized complexity, strategy improvement, Bland’s rule}
}
Document
Distributed Coloring of Graphs with an Optimal Number of Colors
Abstract
This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e. with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so far has focused on coloring graphs of maximum degree Delta with at most Delta+1 colors (or Delta colors when some simple obstructions are forbidden). When Delta is sufficiently large and c >= Delta-k_Delta+1, for some integer k_Delta ~~ sqrt{Delta}-2, we give a distributed algorithm that given a c-colorable graph G of maximum degree Delta, finds a c-coloring of G in min{O((log Delta)^{13/12}log n), 2^{O(log Delta+sqrt{log log n})}} rounds, with high probability. The lower bound Delta-k_Delta+1 is best possible in the sense that for infinitely many values of Delta, we prove that when chi(G) <= Delta-k_Delta, finding an optimal coloring of G requires Omega(n) rounds. Our proof is a light adaptation of a remarkable result of Molloy and Reed, who proved that for Delta large enough, for any c >= Delta-k_Delta deciding whether chi(G) <= c is in P, while Embden-Weinert et al. proved that for c <= Delta-k_Delta-1, the same problem is NP-complete. Note that the sequential and distributed thresholds differ by one.
Our first result covers the case where the chromatic number of the graph ranges between Delta-sqrt{Delta} and Delta+1. Our second result covers a larger range, but gives a weaker bound on the number of colors: For any sufficiently large Delta, and Omega(log Delta) <= k <= Delta/100, we prove that every graph of maximum degree Delta and clique number at most Delta-k can be efficiently colored with at most Delta-epsilon k colors, for some absolute constant epsilon >0, with a randomized algorithm running in O(log n/log log n) rounds with high probability.
Cite as
Étienne Bamas and Louis Esperet. Distributed Coloring of Graphs with an Optimal Number of Colors. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{bamas_et_al:LIPIcs.STACS.2019.10,
author = {Bamas, \'{E}tienne and Esperet, Louis},
title = {{Distributed Coloring of Graphs with an Optimal Number of Colors}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {10:1--10:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.10},
URN = {urn:nbn:de:0030-drops-102496},
doi = {10.4230/LIPIcs.STACS.2019.10},
annote = {Keywords: Graph coloring, distributed algorithm, maximum degree}
}
Document
On the Descriptive Complexity of Color Coding
Abstract
Color coding is an algorithmic technique used in parameterized complexity theory to detect "small" structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable, small color pattern. We transfer color coding to the world of descriptive complexity theory by characterizing - purely in terms of the syntactic structure of describing formulas - when the powerful second-order quantifiers representing a random coloring can be replaced by equivalent, simple first-order formulas. Building on this result, we identify syntactic properties of first-order quantifiers that can be eliminated from formulas describing parameterized problems. The result applies to many packing and embedding problems, but also to the long path problem. Together with a new result on the parameterized complexity of formula families involving only a fixed number of variables, we get that many problems lie in fpt just because of the way they are commonly described using logical formulas.
Cite as
Max Bannach and Till Tantau. On the Descriptive Complexity of Color Coding. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{bannach_et_al:LIPIcs.STACS.2019.11,
author = {Bannach, Max and Tantau, Till},
title = {{On the Descriptive Complexity of Color Coding}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {11:1--11:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.11},
URN = {urn:nbn:de:0030-drops-102509},
doi = {10.4230/LIPIcs.STACS.2019.11},
annote = {Keywords: color coding, descriptive complexity, fixed-parameter tractability, quantifier elimination, para-AC^0}
}
Document
Bounding Quantum-Classical Separations for Classes of Nonlocal Games
Abstract
We bound separations between the entangled and classical values for several classes of nonlocal t-player games. Our motivating question is whether there is a family of t-player XOR games for which the entangled bias is 1 but for which the classical bias goes down to 0, for fixed t. Answering this question would have important consequences in the study of multi-party communication complexity, as a positive answer would imply an unbounded separation between randomized communication complexity with and without entanglement. Our contribution to answering the question is identifying several general classes of games for which the classical bias can not go to zero when the entangled bias stays above a constant threshold. This rules out the possibility of using these games to answer our motivating question. A previously studied set of XOR games, known not to give a positive answer to the question, are those for which there is a quantum strategy that attains value 1 using a so-called Schmidt state. We generalize this class to mod-m games and show that their classical value is always at least 1/m + (m-1)/m t^{1-t}. Secondly, for free XOR games, in which the input distribution is of product form, we show beta(G) >= beta^*(G)^{2^t} where beta(G) and beta^*(G) are the classical and entangled biases of the game respectively. We also introduce so-called line games, an example of which is a slight modification of the Magic Square game, and show that they can not give a positive answer to the question either. Finally we look at two-player unique games and show that if the entangled value is 1-epsilon then the classical value is at least 1-O(sqrt{epsilon log k}) where k is the number of outputs in the game. Our proofs use semidefinite-programming techniques, the Gowers inverse theorem and hypergraph norms.
Cite as
Tom Bannink, Jop Briët, Harry Buhrman, Farrokh Labib, and Troy Lee. Bounding Quantum-Classical Separations for Classes of Nonlocal Games. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 12:1-12:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{bannink_et_al:LIPIcs.STACS.2019.12,
author = {Bannink, Tom and Bri\"{e}t, Jop and Buhrman, Harry and Labib, Farrokh and Lee, Troy},
title = {{Bounding Quantum-Classical Separations for Classes of Nonlocal Games}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {12:1--12:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.12},
URN = {urn:nbn:de:0030-drops-102512},
doi = {10.4230/LIPIcs.STACS.2019.12},
annote = {Keywords: Nonlocal games, communication complexity, bounded separations, semidefinite programming, pseudorandomness, Gowers norms}
}
Document
Token Sliding on Split Graphs
Abstract
We consider the complexity of the Independent Set Reconfiguration problem under the Token Sliding rule. In this problem we are given two independent sets of a graph and are asked if we can transform one to the other by repeatedly exchanging a vertex that is currently in the set with one of its neighbors, while maintaining the set independent. Our main result is to show that this problem is PSPACE-complete on split graphs (and hence also on chordal graphs), thus resolving an open problem in this area.
We then go on to consider the c-Colorable Reconfiguration problem under the same rule, where the constraint is now to maintain the set c-colorable at all times. As one may expect, a simple modification of our reduction shows that this more general problem is PSPACE-complete for all fixed c >= 1 on chordal graphs. Somewhat surprisingly, we show that the same cannot be said for split graphs: we give a polynomial time (n^{O(c)}) algorithm for all fixed values of c, except c=1, for which the problem is PSPACE-complete. We complement our algorithm with a lower bound showing that c-Colorable Reconfiguration is W[2]-hard on split graphs parameterized by c and the length of the solution, as well as a tight ETH-based lower bound for both parameters.
Cite as
Rémy Belmonte, Eun Jung Kim, Michael Lampis, Valia Mitsou, Yota Otachi, and Florian Sikora. Token Sliding on Split Graphs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{belmonte_et_al:LIPIcs.STACS.2019.13,
author = {Belmonte, R\'{e}my and Kim, Eun Jung and Lampis, Michael and Mitsou, Valia and Otachi, Yota and Sikora, Florian},
title = {{Token Sliding on Split Graphs}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {13:1--13:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.13},
URN = {urn:nbn:de:0030-drops-102529},
doi = {10.4230/LIPIcs.STACS.2019.13},
annote = {Keywords: reconfiguration, independent set, split graph}
}
Document
Building Strategies into QBF Proofs
Abstract
Strategy extraction is of paramount importance for quantified Boolean formulas (QBF), both in solving and proof complexity. It extracts (counter)models for a QBF from a run of the solver resp. the proof of the QBF, thereby allowing to certify the solver’s answer resp. establish soundness of the system. So far in the QBF literature, strategy extraction has been algorithmically performed from proofs. Here we devise the first QBF system where (partial) strategies are built into the proof and are piecewise constructed by simple operations along with the derivation.
This has several advantages: (1) lines of our calculus have a clear semantic meaning as they are accompanied by semantic objects; (2) partial strategies are represented succinctly (in contrast to some previous approaches); (3) our calculus has strategy extraction by design; and (4) the partial strategies allow new sound inference steps which are disallowed in previous central QBF calculi such as Q-Resolution and long-distance Q-Resolution.
The last item (4) allows us to show an exponential separation between our new system and the previously studied reductionless long-distance resolution calculus, introduced to model QCDCL solving.
Our approach also naturally lifts to dependency QBFs (DQBF), where it yields the first sound and complete CDCL-type calculus for DQBF, thus opening future avenues into DQBF CDCL solving.
Cite as
Olaf Beyersdorff, Joshua Blinkhorn, and Meena Mahajan. Building Strategies into QBF Proofs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{beyersdorff_et_al:LIPIcs.STACS.2019.14,
author = {Beyersdorff, Olaf and Blinkhorn, Joshua and Mahajan, Meena},
title = {{Building Strategies into QBF Proofs}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {14:1--14:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.14},
URN = {urn:nbn:de:0030-drops-102538},
doi = {10.4230/LIPIcs.STACS.2019.14},
annote = {Keywords: QBF, DQBF, resolution, proof complexity}
}
Document
Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line
Abstract
The online Dial-a-Ride problem is a fundamental online problem in a metric space, where transportation requests appear over time and may be served in any order by a single server with unit speed. Restricted to the real line, online Dial-a-Ride captures natural problems like controlling a personal elevator. Tight results in terms of competitive ratios are known for the general setting and for online TSP on the line (where source and target of each request coincide). In contrast, online Dial-a-Ride on the line has resisted tight analysis so far, even though it is a very natural online problem.
We conduct a tight competitive analysis of the Smartstart algorithm that gave the best known results for the general, metric case. In particular, our analysis yields a new upper bound of 2.94 for open, non-preemptive online Dial-a-Ride on the line, which improves the previous bound of 3.41 [Krumke'00]. The best known lower bound remains 2.04 [SODA'17]. We also show that the known upper bound of 2 [STACS'00] regarding Smartstart’s competitive ratio for closed, non-preemptive online Dial-a-Ride is tight on the line.
Cite as
Alexander Birx and Yann Disser. Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{birx_et_al:LIPIcs.STACS.2019.15,
author = {Birx, Alexander and Disser, Yann},
title = {{Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {15:1--15:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.15},
URN = {urn:nbn:de:0030-drops-102543},
doi = {10.4230/LIPIcs.STACS.2019.15},
annote = {Keywords: dial-a-ride on the line, elevator problem, online algorithms, competitive analysis, smartstart, competitive ratio}
}
Document
Enumerating Minimal Dominating Sets in Triangle-Free Graphs
Abstract
It is a long-standing open problem whether the minimal dominating sets of a graph can be enumerated in output-polynomial time. In this paper we prove that this is the case in triangle-free graphs. This answers a question of Kanté et al. Additionally, we show that deciding if a set of vertices of a bipartite graph can be completed into a minimal dominating set is a NP-complete problem.
Cite as
Marthe Bonamy, Oscar Defrain, Marc Heinrich, and Jean-Florent Raymond. Enumerating Minimal Dominating Sets in Triangle-Free Graphs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{bonamy_et_al:LIPIcs.STACS.2019.16,
author = {Bonamy, Marthe and Defrain, Oscar and Heinrich, Marc and Raymond, Jean-Florent},
title = {{Enumerating Minimal Dominating Sets in Triangle-Free Graphs}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {16:1--16:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.16},
URN = {urn:nbn:de:0030-drops-102557},
doi = {10.4230/LIPIcs.STACS.2019.16},
annote = {Keywords: Enumeration algorithms, output-polynomial algorithms, minimal dominating set, triangle-free graphs, split graphs}
}
Document
Sparsification of Binary CSPs
Abstract
A cut epsilon-sparsifier of a weighted graph G is a re-weighted subgraph of G of (quasi)linear size that preserves the size of all cuts up to a multiplicative factor of epsilon. Since their introduction by Benczúr and Karger [STOC'96], cut sparsifiers have proved extremely influential and found various applications. Going beyond cut sparsifiers, Filtser and Krauthgamer [SIDMA'17] gave a precise classification of which binary Boolean CSPs are sparsifiable. In this paper, we extend their result to binary CSPs on arbitrary finite domains.
Cite as
Silvia Butti and Stanislav Živný. Sparsification of Binary CSPs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 17:1-17:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{butti_et_al:LIPIcs.STACS.2019.17,
author = {Butti, Silvia and \v{Z}ivn\'{y}, Stanislav},
title = {{Sparsification of Binary CSPs}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {17:1--17:8},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.17},
URN = {urn:nbn:de:0030-drops-102564},
doi = {10.4230/LIPIcs.STACS.2019.17},
annote = {Keywords: constraint satisfaction problems, minimum cuts, sparsification}
}
Document
Tractable QBF by Knowledge Compilation
Abstract
We generalize several tractability results concerning the tractability of Quantified Boolean Formulas (QBF) with restricted underlying structure. To this end, we introduce a notion of width for structured DNNF which are a class of Boolean circuits heavily studied in knowledge compilation, a subarea of artificial intelligence. We then show that structured DNNF allow quantifier elimination with a size blow-up depending only on the width of the DNNF and not its size. Using known algorithms transforming restricted CNF-formulas into deterministic DNNF, we apply this result to generalize several results for counting and decision on QBF. We also complement these results with lower bounds that show that our definitions and results are essentially optimal in several senses.
Cite as
Florent Capelli and Stefan Mengel. Tractable QBF by Knowledge Compilation. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{capelli_et_al:LIPIcs.STACS.2019.18,
author = {Capelli, Florent and Mengel, Stefan},
title = {{Tractable QBF by Knowledge Compilation}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {18:1--18:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.18},
URN = {urn:nbn:de:0030-drops-102571},
doi = {10.4230/LIPIcs.STACS.2019.18},
annote = {Keywords: QBF, knowledge compilation, parameterized algorithms}
}
Document
A Tight Extremal Bound on the Lovász Cactus Number in Planar Graphs
Abstract
A cactus graph is a graph in which any two cycles are edge-disjoint. We present a constructive proof of the fact that any plane graph G contains a cactus subgraph C where C contains at least a 1/6 fraction of the triangular faces of G. We also show that this ratio cannot be improved by showing a tight lower bound. Together with an algorithm for linear matroid parity, our bound implies two approximation algorithms for computing "dense planar structures" inside any graph: (i) A 1/6 approximation algorithm for, given any graph G, finding a planar subgraph with a maximum number of triangular faces; this improves upon the previous 1/11-approximation; (ii) An alternate (and arguably more illustrative) proof of the 4/9 approximation algorithm for finding a planar subgraph with a maximum number of edges.
Our bound is obtained by analyzing a natural local search strategy and heavily exploiting the exchange arguments. Therefore, this suggests the power of local search in handling problems of this kind.
Cite as
Parinya Chalermsook, Andreas Schmid, and Sumedha Uniyal. A Tight Extremal Bound on the Lovász Cactus Number in Planar Graphs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{chalermsook_et_al:LIPIcs.STACS.2019.19,
author = {Chalermsook, Parinya and Schmid, Andreas and Uniyal, Sumedha},
title = {{A Tight Extremal Bound on the Lov\'{a}sz Cactus Number in Planar Graphs}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {19:1--19:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.19},
URN = {urn:nbn:de:0030-drops-102583},
doi = {10.4230/LIPIcs.STACS.2019.19},
annote = {Keywords: Graph Drawing, Matroid Matching, Maximum Planar Subgraph, Local Search Algorithms}
}
Document
Average-Case Completeness in Tag Systems
Abstract
To prove average-case NP-completeness for a problem, we must choose a known average-case complete problem and reduce it to that problem. Unfortunately, the set of options to choose from is far smaller than for standard (worst-case) NP-completeness. In an effort to help remedy this we focus on tag systems, which due to their extreme simplicity have been a target for other types of reductions for many problems including the matrix mortality problem, the Post correspondence problem, the universality of cellular automaton Rule 110, and all of the smallest universal single-tape Turing machines. Here we show that a tag system can efficiently simulate a Turing machine even when the input is provided in an extremely simple encoding which adds just log n carefully set bits to encode an arbitrary Turing machine input of length n. As a result we show that the bounded halting problem for nondeterministic tag systems is average-case NP-complete. This result is unexpected when one considers that in the current state of the art for simple universal systems it had appeared that there was a trade-off whereby simpler systems required more complicated input encodings. In other words, although simple systems can compute interesting things, they had appeared to require very carefully encoded inputs in order to do so. Our result surprisingly goes in the opposite direction by giving the first average-case completeness result for such a simple model of computation. In ongoing work we have already found applications of our result having used it to give average-case NP-completeness results for a 2D generalization of the Collatz function, a nondeterministic version of the 2D elementary functions studied by Koiran and Moore, 3D piecewise affine maps, and bounded Post correspondence problem instances that use simpler word pairs than previous results.
Cite as
Matthew Cook and Turlough Neary. Average-Case Completeness in Tag Systems. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{cook_et_al:LIPIcs.STACS.2019.20,
author = {Cook, Matthew and Neary, Turlough},
title = {{Average-Case Completeness in Tag Systems}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {20:1--20:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.20},
URN = {urn:nbn:de:0030-drops-102590},
doi = {10.4230/LIPIcs.STACS.2019.20},
annote = {Keywords: average-case NP-completeness, encoding complexity, tag system, bounded halting problem}
}
Document
Pairwise Preferences in the Stable Marriage Problem
Abstract
We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to declare a draw or even withdraw from such a comparison. This freedom is then gradually restricted as we specify six stages of orderedness in the preferences, ending with the classical case of strictly ordered lists. We study all cases occurring when combining the three known notions of stability - weak, strong and super-stability - under the assumption that each side of the bipartite market obtains one of the six degrees of orderedness. By designing three polynomial algorithms and two NP-completeness proofs we determine the complexity of all cases not yet known, and thus give an exact boundary in terms of preference structure between tractable and intractable cases.
Cite as
Ágnes Cseh and Attila Juhos. Pairwise Preferences in the Stable Marriage Problem. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{cseh_et_al:LIPIcs.STACS.2019.21,
author = {Cseh, \'{A}gnes and Juhos, Attila},
title = {{Pairwise Preferences in the Stable Marriage Problem}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {21:1--21:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.21},
URN = {urn:nbn:de:0030-drops-102603},
doi = {10.4230/LIPIcs.STACS.2019.21},
annote = {Keywords: stable marriage, intransitivity, acyclic preferences, poset, weakly stable matching, strongly stable matching, super stable matching}
}
Document
Closure Properties of Synchronized Relations
Abstract
A standard approach to define k-ary word relations over a finite alphabet A is through k-tape finite state automata that recognize regular languages L over {1, ..., k} x A, where (i,a) is interpreted as reading letter a from tape i. Accordingly, a word w in L denotes the tuple (u_1, ..., u_k) in (A^*)^k in which u_i is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of rational relations, enforcing restrictions on the reading regime from the tapes, which we call synchronization, yields various sub-classes of relations. Such synchronization restrictions are imposed through regular properties on the projection of the language L onto {1, ..., k}. In this way, for each regular language C subseteq {1, ..., k}^*, one obtains a class Rel({C}) of relations. Synchronous, Recognizable, and Length-preserving rational relations are all examples of classes that can be defined in this way.
We study basic properties of these classes of relations, in terms of closure under intersection, complement, concatenation, Kleene star and projection. We characterize the classes with each closure property. For the binary case (k=2) this yields effective procedures.
Cite as
María Emilia Descotte, Diego Figueira, and Santiago Figueira. Closure Properties of Synchronized Relations. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{descotte_et_al:LIPIcs.STACS.2019.22,
author = {Descotte, Mar{\'\i}a Emilia and Figueira, Diego and Figueira, Santiago},
title = {{Closure Properties of Synchronized Relations}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {22:1--22:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.22},
URN = {urn:nbn:de:0030-drops-102614},
doi = {10.4230/LIPIcs.STACS.2019.22},
annote = {Keywords: synchronized word relations, rational, closure, characterization, intersection, complement, Kleene star, concatenation}
}
Document
Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts
Abstract
We suggest necessary conditions of soficness of multidimensional shifts formulated in terms of resource-bounded Kolmogorov complexity. Using this technique we provide examples of effective and non-sofic shifts on Z^2 with very low block complexity: the number of globally admissible patterns of size n x n grows only as a polynomial in n.
Cite as
Julien Destombes and Andrei Romashchenko. Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{destombes_et_al:LIPIcs.STACS.2019.23,
author = {Destombes, Julien and Romashchenko, Andrei},
title = {{Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {23:1--23:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.23},
URN = {urn:nbn:de:0030-drops-102624},
doi = {10.4230/LIPIcs.STACS.2019.23},
annote = {Keywords: Sofic shifts, Block complexity, Kolmogorov complexity}
}
Document
Constant-Time Retrieval with O(log m) Extra Bits
Abstract
For a set U (the universe), retrieval is the following problem. Given a finite subset S subseteq U of size m and f : S -> {0,1}^r for a small constant r, build a data structure D_f with the property that for a suitable query algorithm query we have query(D_f,x) = f(x) for all x in S. For x in U setminus S the value query(D_f,x) is arbitrary in {0,1}^r. The number of bits needed for D_f should be (1+epsilon)r m with overhead epsilon = epsilon(m) >= 0 as small as possible, while the query time should be small. Of course, the time for constructing D_f is relevant as well.
We assume fully random hash functions on U with constant evaluation time are available. It is known that with epsilon ~= 0.09 one can achieve linear construction time and constant query time, and with overhead epsilon_k ~= e^{-k} it is possible to have O(k) query time and O(m^{1+alpha}) construction time, for arbitrary alpha>0. Furthermore, a theoretical construction with epsilon =O((log log m)/sqrt{log m}) gives constant query time and linear construction time. Known constructions avoiding all overhead, except for a seed value of size O(log log m), require logarithmic query time.
In this paper, we present a method for treating the retrieval problem with overhead epsilon = O((log m)/m), which corresponds to O(1) extra memory words (O(log m) bits), and an extremely simple, constant-time query operation. The price to pay is a construction time of O(m^2). We employ the usual framework for retrieval data structures, where construction is effected by solving a sparse linear system of equations over the 2-element field F_2 and a query is effected by a dot product calculation. Our main technical contribution is the design and analysis of a new and natural family of sparse random linear systems with m equations and (1+epsilon)m variables, which combines good locality properties with high probability of having full rank.
Paying a larger overhead of epsilon = O((log m)/m^alpha), the construction time can be reduced to O(m^{1+alpha}) for arbitrary constant 0 < alpha < 1. In combination with an adaptation of known techniques for solving sparse linear systems of equations, our approach leads to a highly practical algorithm for retrieval. In a particular benchmark with m = 10^7 we achieve an order-of-magnitude improvement over previous techniques with epsilon = 0.24% instead of the previously best result of epsilon ~= 3%, with better query time and no significant sacrifices in construction time.
Cite as
Martin Dietzfelbinger and Stefan Walzer. Constant-Time Retrieval with O(log m) Extra Bits. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{dietzfelbinger_et_al:LIPIcs.STACS.2019.24,
author = {Dietzfelbinger, Martin and Walzer, Stefan},
title = {{Constant-Time Retrieval with O(log m) Extra Bits}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {24:1--24:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.24},
URN = {urn:nbn:de:0030-drops-102639},
doi = {10.4230/LIPIcs.STACS.2019.24},
annote = {Keywords: Retrieval, Hashing, Succinct Data Structure, Randomised Data Structure, Structured Gaussian Elimination, Method of Four Russians}
}
Document
Complexity of the Steiner Network Problem with Respect to the Number of Terminals
Abstract
In the Directed Steiner Network problem we are given an arc-weighted digraph G, a set of terminals T subseteq V(G) with |T|=q, and an (unweighted) directed request graph R with V(R)=T. Our task is to output a subgraph H subseteq G of the minimum cost such that there is a directed path from s to t in H for all st in A(R).
It is known that the problem can be solved in time |V(G)|^{O(|A(R)|)} [Feldman and Ruhl, SIAM J. Comput. 2006] and cannot be solved in time |V(G)|^{o(|A(R)|)} even if G is planar, unless the Exponential-Time Hypothesis (ETH) fails [Chitnis et al., SODA 2014]. However, the reduction (and other reductions showing hardness of the problem) only shows that the problem cannot be solved in time |V(G)|^{o(q)}, unless ETH fails. Therefore, there is a significant gap in the complexity with respect to q in the exponent.
We show that Directed Steiner Network is solvable in time f(q)* |V(G)|^{O(c_g * q)}, where c_g is a constant depending solely on the genus of G and f is a computable function. We complement this result by showing that there is no f(q)* |V(G)|^{o(q^2/ log q)} algorithm for any function f for the problem on general graphs, unless ETH fails.
Cite as
Eduard Eiben, Dušan Knop, Fahad Panolan, and Ondřej Suchý. Complexity of the Steiner Network Problem with Respect to the Number of Terminals. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{eiben_et_al:LIPIcs.STACS.2019.25,
author = {Eiben, Eduard and Knop, Du\v{s}an and Panolan, Fahad and Such\'{y}, Ond\v{r}ej},
title = {{Complexity of the Steiner Network Problem with Respect to the Number of Terminals}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {25:1--25:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.25},
URN = {urn:nbn:de:0030-drops-102642},
doi = {10.4230/LIPIcs.STACS.2019.25},
annote = {Keywords: Directed Steiner Network, Planar Graphs, Parameterized Algorithms, Bounded Genus, Exponential Time Hypothesis}
}
Document
Space Lower Bounds for the Signal Detection Problem
Abstract
Many shared memory algorithms have to deal with the problem of determining whether the value of a shared object has changed in between two successive accesses of that object by a process when the responses from both are the same. Motivated by this problem, we define the signal detection problem, which can be studied on a purely combinatorial level. Consider a system with n+1 processes consisting of n readers and one signaller. The processes communicate through a shared blackboard that can store a value from a domain of size m. Processes are scheduled by an adversary. When scheduled, a process reads the blackboard, modifies its contents arbitrarily, and, provided it is a reader, returns a Boolean value. A reader must return true if the signaller has taken a step since the reader’s preceding step; otherwise it must return false.
Intuitively, in a system with n processes, signal detection should require at least n bits of shared information, i.e., m >= 2^n. But a proof of this conjecture remains elusive. We prove a lower bound of m >= n^2, as well as a tight lower bound of m >= 2^n for two restricted versions of the problem, where the processes are oblivious or where the signaller always resets the blackboard to the same fixed value. We also consider a one-shot version of the problem, where each reader takes at most two steps. In this case, we prove that it is necessary and sufficient that the blackboard can store m=n+1 values.
Cite as
Faith Ellen, Rati Gelashvili, Philipp Woelfel, and Leqi Zhu. Space Lower Bounds for the Signal Detection Problem. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{ellen_et_al:LIPIcs.STACS.2019.26,
author = {Ellen, Faith and Gelashvili, Rati and Woelfel, Philipp and Zhu, Leqi},
title = {{Space Lower Bounds for the Signal Detection Problem}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {26:1--26:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.26},
URN = {urn:nbn:de:0030-drops-102654},
doi = {10.4230/LIPIcs.STACS.2019.26},
annote = {Keywords: Signal detection, ABA problem, space complexity, lower bound}
}
Document
Progressive Algorithms for Domination and Independence
Abstract
We consider a generic algorithmic paradigm that we call progressive exploration, which can be used to develop simple and efficient parameterized graph algorithms. We identify two model-theoretic properties that lead to efficient progressive algorithms, namely variants of the Helly property and stability. We demonstrate our approach by giving linear-time fixed-parameter algorithms for the Distance-r Dominating Set problem (parameterized by the solution size) in a wide variety of restricted graph classes, such as powers of nowhere dense classes, map graphs, and (for r=1) biclique-free graphs. Similarly, for the Distance-r Independent Set problem the technique can be used to give a linear-time fixed-parameter algorithm on any nowhere dense class. Despite the simplicity of the method, in several cases our results extend known boundaries of tractability for the considered problems and improve the best known running times.
Cite as
Grzegorz Fabiański, Michał Pilipczuk, Sebastian Siebertz, and Szymon Toruńczyk. Progressive Algorithms for Domination and Independence. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{fabianski_et_al:LIPIcs.STACS.2019.27,
author = {Fabia\'{n}ski, Grzegorz and Pilipczuk, Micha{\l} and Siebertz, Sebastian and Toru\'{n}czyk, Szymon},
title = {{Progressive Algorithms for Domination and Independence}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {27:1--27:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.27},
URN = {urn:nbn:de:0030-drops-102660},
doi = {10.4230/LIPIcs.STACS.2019.27},
annote = {Keywords: Dominating Set, Independent Set, nowhere denseness, stability, fixed-parameter tractability}
}
Document
Modification to Planarity is Fixed Parameter Tractable
Abstract
A replacement action is a function L that maps each k-vertex labeled graph to another k-vertex graph. We consider a general family of graph modification problems, called L-Replacement to C, where the input is a graph G and the question is whether it is possible to replace in G some k-vertex subgraph H of it by L(H) so that the new graph belongs to the graph class C. L-Replacement to C can simulate several modification operations such as edge addition, edge removal, edge editing, and diverse completion and superposition operations. In this paper, we prove that for any action L, if C is the class of planar graphs, there is an algorithm that solves L-Replacement to C in O(|G|^{2}) steps. We also present several applications of our approach to related problems.
Cite as
Fedor V. Fomin, Petr A. Golovach, and Dimitrios M. Thilikos. Modification to Planarity is Fixed Parameter Tractable. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{fomin_et_al:LIPIcs.STACS.2019.28,
author = {Fomin, Fedor V. and Golovach, Petr A. and Thilikos, Dimitrios M.},
title = {{Modification to Planarity is Fixed Parameter Tractable}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {28:1--28:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.28},
URN = {urn:nbn:de:0030-drops-102677},
doi = {10.4230/LIPIcs.STACS.2019.28},
annote = {Keywords: Modification problems, Planar graphs, Irrelevant vertex technique}
}
Document
Visibly Pushdown Languages over Sliding Windows
Abstract
We investigate the class of visibly pushdown languages in the sliding window model. A sliding window algorithm for a language L receives a stream of symbols and has to decide at each time step whether the suffix of length n belongs to L or not. The window size n is either a fixed number (in the fixed-size model) or can be controlled by an adversary in a limited way (in the variable-size model). The main result of this paper states that for every visibly pushdown language the space complexity in the variable-size sliding window model is either constant, logarithmic or linear in the window size. This extends previous results for regular languages.
Cite as
Moses Ganardi. Visibly Pushdown Languages over Sliding Windows. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{ganardi:LIPIcs.STACS.2019.29,
author = {Ganardi, Moses},
title = {{Visibly Pushdown Languages over Sliding Windows}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {29:1--29:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.29},
URN = {urn:nbn:de:0030-drops-102688},
doi = {10.4230/LIPIcs.STACS.2019.29},
annote = {Keywords: visibly pushdown languages, sliding windows, rational transductions}
}
Document
Fast and Longest Rollercoasters
Abstract
For k >= 3, a k-rollercoaster is a sequence of numbers whose every maximal contiguous subsequence, that is increasing or decreasing, has length at least k; 3-rollercoasters are called simply rollercoasters. Given a sequence of distinct real numbers, we are interested in computing its maximum-length (not necessarily contiguous) subsequence that is a k-rollercoaster. Biedl et al. (2018) have shown that each sequence of n distinct real numbers contains a rollercoaster of length at least ceil[n/2] for n>7, and that a longest rollercoaster contained in such a sequence can be computed in O(n log n)-time (or faster, in O(n log log n) time, when the input sequence is a permutation of {1,...,n}). They have also shown that every sequence of n >=slant (k-1)^2+1 distinct real numbers contains a k-rollercoaster of length at least n/(2(k-1)) - 3k/2, and gave an O(nk log n)-time (respectively, O(n k log log n)-time) algorithm computing a longest k-rollercoaster in a sequence of length n (respectively, a permutation of {1,...,n}).
In this paper, we give an O(nk^2)-time algorithm computing the length of a longest k-rollercoaster contained in a sequence of n distinct real numbers; hence, for constant k, our algorithm computes the length of a longest k-rollercoaster in optimal linear time. The algorithm can be easily adapted to output the respective k-rollercoaster. In particular, this improves the results of Biedl et al. (2018), by showing that a longest rollercoaster can be computed in optimal linear time. We also present an algorithm computing the length of a longest k-rollercoaster in O(n log^2 n)-time, that is, subquadratic even for large values of k <= n. Again, the rollercoaster can be easily retrieved. Finally, we show an Omega(n log k) lower bound for the number of comparisons in any comparison-based algorithm computing the length of a longest k-rollercoaster.
Cite as
Paweł Gawrychowski, Florin Manea, and Radosław Serafin. Fast and Longest Rollercoasters. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{gawrychowski_et_al:LIPIcs.STACS.2019.30,
author = {Gawrychowski, Pawe{\l} and Manea, Florin and Serafin, Rados{\l}aw},
title = {{Fast and Longest Rollercoasters}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {30:1--30:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.30},
URN = {urn:nbn:de:0030-drops-102694},
doi = {10.4230/LIPIcs.STACS.2019.30},
annote = {Keywords: sequences, alternating runs, patterns in permutations}
}
Document
Wealth Inequality and the Price of Anarchy
Abstract
The price of anarchy quantifies the degradation of social welfare in games due to the lack of a centralized authority that can enforce the optimal outcome. It is known that, in certain games, such effects can be ameliorated via tolls or taxes. This leads to a natural, but largely unexplored, question: what is the effect of such transfers on social inequality? We study this question in nonatomic congestion games, arguably one of the most thoroughly studied settings from the perspective of the price of anarchy. We introduce a new model that incorporates the income distribution of the population and captures the income elasticity of travel time (i.e., how does loss of time translate to lost income). This allows us to argue about the equality of wealth distribution both before and after employing a mechanism. We establish that, under reasonable assumptions, tolls always increase inequality in symmetric congestion games under any reasonable metric of inequality such as the Gini index. We introduce the inequity index, a novel measure for quantifying the magnitude of these forces towards a more unbalanced wealth distribution and show it has good normative properties (robustness to scaling of income, no-regret learning). We analyze inequity both in theoretical settings (Pigou’s network under various wealth distributions) as well as experimental ones (based on a large scale field experiment in Singapore). Finally, we provide an algorithm for computing optimal tolls for any point of the trade-off of relative importance of efficiency and equality. We conclude with a discussion of our findings in the context of theories of justice as developed in contemporary social sciences and present several directions for future research.
Cite as
Kurtuluş Gemici, Elias Koutsoupias, Barnabé Monnot, Christos H. Papadimitriou, and Georgios Piliouras. Wealth Inequality and the Price of Anarchy. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{gemici_et_al:LIPIcs.STACS.2019.31,
author = {Gemici, Kurtulu\c{s} and Koutsoupias, Elias and Monnot, Barnab\'{e} and Papadimitriou, Christos H. and Piliouras, Georgios},
title = {{Wealth Inequality and the Price of Anarchy}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {31:1--31:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.31},
URN = {urn:nbn:de:0030-drops-102707},
doi = {10.4230/LIPIcs.STACS.2019.31},
annote = {Keywords: congestion games, inequality}
}
Document
Lean Tree-Cut Decompositions: Obstructions and Algorithms
Abstract
The notion of tree-cut width has been introduced by Wollan in [The structure of graphs not admitting a fixed immersion, Journal of Combinatorial Theory, Series B, 110:47 - 66, 2015]. It is defined via tree-cut decompositions, which are tree-like decompositions that highlight small (edge) cuts in a graph. In that sense, tree-cut decompositions can be seen as an edge-version of tree-decompositions and have algorithmic applications on problems that remain intractable on graphs of bounded treewidth. In this paper, we prove that every graph admits an optimal tree-cut decomposition that satisfies a certain Menger-like condition similar to that of the lean tree decompositions of Thomas [A Menger-like property of tree-width: The finite case, Journal of Combinatorial Theory, Series B, 48(1):67 - 76, 1990]. This allows us to give, for every k in N, an upper-bound on the number immersion-minimal graphs of tree-cut width k. Our results imply the constructive existence of a linear FPT-algorithm for tree-cut width.
Cite as
Archontia C. Giannopoulou, O-joung Kwon, Jean-Florent Raymond, and Dimitrios M. Thilikos. Lean Tree-Cut Decompositions: Obstructions and Algorithms. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{giannopoulou_et_al:LIPIcs.STACS.2019.32,
author = {Giannopoulou, Archontia C. and Kwon, O-joung and Raymond, Jean-Florent and Thilikos, Dimitrios M.},
title = {{Lean Tree-Cut Decompositions: Obstructions and Algorithms}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {32:1--32:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.32},
URN = {urn:nbn:de:0030-drops-102716},
doi = {10.4230/LIPIcs.STACS.2019.32},
annote = {Keywords: tree-cut width, lean decompositions, immersions, obstructions, parameterized algorithms}
}
Document
Dispersing Obnoxious Facilities on a Graph
Abstract
We study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance delta from each other.
We investigate the complexity of this problem in terms of the rational parameter delta. The problem is polynomially solvable, if the numerator of delta is 1 or 2, while all other cases turn out to be NP-hard.
Cite as
Alexander Grigoriev, Tim A. Hartmann, Stefan Lendl, and Gerhard J. Woeginger. Dispersing Obnoxious Facilities on a Graph. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 33:1-33:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{grigoriev_et_al:LIPIcs.STACS.2019.33,
author = {Grigoriev, Alexander and Hartmann, Tim A. and Lendl, Stefan and Woeginger, Gerhard J.},
title = {{Dispersing Obnoxious Facilities on a Graph}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {33:1--33:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.33},
URN = {urn:nbn:de:0030-drops-102729},
doi = {10.4230/LIPIcs.STACS.2019.33},
annote = {Keywords: algorithms, complexity, optimization, graph theory, facility location}
}
Document
Reachability in O(log n) Genus Graphs is in Unambiguous Logspace
Abstract
We show that given an embedding of an O(log n) genus graph G and two vertices s and t in G, deciding if there is a path from s to t in G is in unambiguous logarithmic space.
Unambiguous computation is a restriction of nondeterministic computation where the nondeterministic machine has at most one accepting computation path on each input. An important fundamental question in computational complexity theory is whether this is an actual restriction or are unambiguous computations as powerful as general nondeterminism. We investigate this problem in the domain of logarithmic space bounded computations, where the corresponding unambiguous and general nondeterministic classes are UL and NL respectively.
In 1997 Reinhardt and Allender showed that NL and UL are equal in a non-uniform model. More specifically they showed that if one can efficiently construct an O(log n)-bit min-unique weight function for a graph, then these classes are equal unconditionally as well. In other words, they gave a UL algorithm to solve reachability in graphs with a min-unique weight assignment. Using this approach reachability in various classes of graphs such as planar graphs, constant genus graphs, minor free graphs, etc., have been shown to be in UL by devising min-unique weight functions for those classes.
In this paper we improve these results by constructing a min-unique weight function for O(log n) genus graphs. We define signature of a path in a graph as the parity of the number of crossings of that path with respect to each handle of the surface on which the graph is embedded. We construct our weight function in two steps. First we ensure that between any pair of vertices, amongst all paths having the same signature, the minimum weight path is unique. Now since in a genus g graph there are 2^{2g} many possible signatures, we use the hashing scheme of Fredman, Komlós and Szemerédi to isolate a unique minimum weight path among these 2^{2g} many paths isolated in the first step.
Cite as
Chetan Gupta, Vimal Raj Sharma, and Raghunath Tewari. Reachability in O(log n) Genus Graphs is in Unambiguous Logspace. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 34:1-34:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{gupta_et_al:LIPIcs.STACS.2019.34,
author = {Gupta, Chetan and Sharma, Vimal Raj and Tewari, Raghunath},
title = {{Reachability in O(log n) Genus Graphs is in Unambiguous Logspace}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {34:1--34:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.34},
URN = {urn:nbn:de:0030-drops-102730},
doi = {10.4230/LIPIcs.STACS.2019.34},
annote = {Keywords: logspace unambiguity, high genus, path isolation}
}
Document
Dominating Sets and Connected Dominating Sets in Dynamic Graphs
Abstract
In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions and edge deletions in time O(Delta * polylog n) per update, where Delta is the maximum vertex degree in the graph. In both cases, we achieve an approximation ratio of O(log n), which is optimal up to a constant factor (under the assumption that P != NP). Although those two problems have been widely studied in the static and in the distributed settings, to the best of our knowledge we are the first to present efficient algorithms in the dynamic setting.
As a further application of our approach, we also present an algorithm that maintains a Minimal Dominating Set in O(min(Delta, sqrt{m})) per update.
Cite as
Niklas Hjuler, Giuseppe F. Italiano, Nikos Parotsidis, and David Saulpic. Dominating Sets and Connected Dominating Sets in Dynamic Graphs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{hjuler_et_al:LIPIcs.STACS.2019.35,
author = {Hjuler, Niklas and Italiano, Giuseppe F. and Parotsidis, Nikos and Saulpic, David},
title = {{Dominating Sets and Connected Dominating Sets in Dynamic Graphs}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {35:1--35:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.35},
URN = {urn:nbn:de:0030-drops-102741},
doi = {10.4230/LIPIcs.STACS.2019.35},
annote = {Keywords: Dominating Set, Connected Dominating Set, Dynamic Graph Algorithms}
}
Document
On Kernelization for Edge Dominating Set under Structural Parameters
Abstract
In the NP-hard Edge Dominating Set problem (EDS) we are given a graph G=(V,E) and an integer k, and need to determine whether there is a set F subseteq E of at most k edges that are incident with all (other) edges of G. It is known that this problem is fixed-parameter tractable and admits a polynomial kernelization when parameterized by k. A caveat for this parameter is that it needs to be large, i.e., at least equal to half the size of a maximum matching of G, for instances not to be trivially negative. Motivated by this, we study the existence of polynomial kernelizations for EDS when parameterized by structural parameters that may be much smaller than k.
Unfortunately, at first glance this looks rather hopeless: Even when parameterized by the deletion distance to a disjoint union of paths P_3 of length two there is no polynomial kernelization (under standard assumptions), ruling out polynomial kernelizations for many smaller parameters like the feedback vertex set size. In contrast, somewhat surprisingly, there is a polynomial kernelization for deletion distance to a disjoint union of paths P_5 of length four. As our main result, we fully classify for all finite sets H of graphs, whether a kernel size polynomial in |X| is possible when given X such that each connected component of G-X is isomorphic to a graph in H.
Cite as
Eva-Maria C. Hols and Stefan Kratsch. On Kernelization for Edge Dominating Set under Structural Parameters. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{hols_et_al:LIPIcs.STACS.2019.36,
author = {Hols, Eva-Maria C. and Kratsch, Stefan},
title = {{On Kernelization for Edge Dominating Set under Structural Parameters}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {36:1--36:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.36},
URN = {urn:nbn:de:0030-drops-102752},
doi = {10.4230/LIPIcs.STACS.2019.36},
annote = {Keywords: Edge dominating set, kernelization, structural parameters}
}
Document
Compressed Decision Problems in Hyperbolic Groups
Abstract
We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight-line programs defined over a finite generating set for the group. We prove also that, for any infinite hyperbolic group G, the compressed knapsack problem in G is NP-complete.
Cite as
Derek Holt, Markus Lohrey, and Saul Schleimer. Compressed Decision Problems in Hyperbolic Groups. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{holt_et_al:LIPIcs.STACS.2019.37,
author = {Holt, Derek and Lohrey, Markus and Schleimer, Saul},
title = {{Compressed Decision Problems in Hyperbolic Groups}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {37:1--37:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.37},
URN = {urn:nbn:de:0030-drops-102766},
doi = {10.4230/LIPIcs.STACS.2019.37},
annote = {Keywords: hyperbolic groups, algorithms for compressed words, circuit evaluation problems}
}
Document
How to Secure Matchings Against Edge Failures
Abstract
Suppose we are given a bipartite graph that admits a perfect matching and an adversary may delete any edge from the graph with the intention of destroying all perfect matchings. We consider the task of adding a minimum cost edge-set to the graph, such that the adversary never wins. We show that this problem is equivalent to covering a digraph with non-trivial strongly connected components at minimal cost. We provide efficient exact and approximation algorithms for this task. In particular, for the unit-cost problem, we give a log_2 n-factor approximation algorithm and a polynomial-time algorithm for chordal-bipartite graphs. Furthermore, we give a fixed parameter algorithm for the problem parameterized by the treewidth of the input graph. For general non-negative weights we give tight upper and lower approximation bounds relative to the Directed Steiner Forest problem. Additionally we prove a dichotomy theorem characterizing minor-closed graph classes which allow for a polynomial-time algorithm. To obtain our results, we exploit a close relation to the classical Strong Connectivity Augmentation problem as well as directed Steiner problems.
Cite as
Felix Hommelsheim, Moritz Mühlenthaler, and Oliver Schaudt. How to Secure Matchings Against Edge Failures. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{hommelsheim_et_al:LIPIcs.STACS.2019.38,
author = {Hommelsheim, Felix and M\"{u}hlenthaler, Moritz and Schaudt, Oliver},
title = {{How to Secure Matchings Against Edge Failures}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {38:1--38:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.38},
URN = {urn:nbn:de:0030-drops-102772},
doi = {10.4230/LIPIcs.STACS.2019.38},
annote = {Keywords: Matchings, Robustness, Connectivity Augmentation, Graph Algorithms, Treewidth}
}
Document
A Deterministic Polynomial Kernel for Odd Cycle Transversal and Vertex Multiway Cut in Planar Graphs
Abstract
We show that Odd Cycle Transversal and Vertex Multiway Cut admit deterministic polynomial kernels when restricted to planar graphs and parameterized by the solution size. This answers a question of Saurabh. On the way to these results, we provide an efficient sparsification routine in the flavor of the sparsification routine used for the Steiner Tree problem in planar graphs (FOCS 2014). It differs from the previous work because it preserves the existence of low-cost subgraphs that are not necessarily Steiner trees in the original plane graph, but structures that turn into (supergraphs of) Steiner trees after adding all edges between pairs of vertices that lie on a common face. We also show connections between Vertex Multiway Cut and the Vertex Planarization problem, where the existence of a polynomial kernel remains an important open problem.
Cite as
Bart M. P. Jansen, Marcin Pilipczuk, and Erik Jan van Leeuwen. A Deterministic Polynomial Kernel for Odd Cycle Transversal and Vertex Multiway Cut in Planar Graphs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 39:1-39:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{jansen_et_al:LIPIcs.STACS.2019.39,
author = {Jansen, Bart M. P. and Pilipczuk, Marcin and van Leeuwen, Erik Jan},
title = {{A Deterministic Polynomial Kernel for Odd Cycle Transversal and Vertex Multiway Cut in Planar Graphs}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {39:1--39:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.39},
URN = {urn:nbn:de:0030-drops-102783},
doi = {10.4230/LIPIcs.STACS.2019.39},
annote = {Keywords: planar graphs, kernelization, odd cycle transversal, multiway cut}
}
Document
A Characterization of Subshifts with Computable Language
Abstract
Subshifts are sets of colorings of Z^d by a finite alphabet that avoid some family of forbidden patterns. We investigate here some analogies with group theory that were first noticed by the first author. In particular we prove several theorems on subshifts inspired by Higman’s embedding theorems of group theory, among which, the fact that subshifts with a computable language can be obtained as restrictions of minimal subshifts of finite type.
Cite as
Emmanuel Jeandel and Pascal Vanier. A Characterization of Subshifts with Computable Language. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{jeandel_et_al:LIPIcs.STACS.2019.40,
author = {Jeandel, Emmanuel and Vanier, Pascal},
title = {{A Characterization of Subshifts with Computable Language}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {40:1--40:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.40},
URN = {urn:nbn:de:0030-drops-102798},
doi = {10.4230/LIPIcs.STACS.2019.40},
annote = {Keywords: subshifts, computability, Enumeration degree, Turing degree, minimal subshifts}
}
Document
Lower Bounds for DeMorgan Circuits of Bounded Negation Width
Abstract
We consider Boolean circuits over {or, and, neg} with negations applied only to input variables. To measure the "amount of negation" in such circuits, we introduce the concept of their "negation width". In particular, a circuit computing a monotone Boolean function f(x_1,...,x_n) has negation width w if no nonzero term produced (purely syntactically) by the circuit contains more than w distinct negated variables. Circuits of negation width w=0 are equivalent to monotone Boolean circuits, while those of negation width w=n have no restrictions. Our motivation is that already circuits of moderate negation width w=n^{epsilon} for an arbitrarily small constant epsilon>0 can be even exponentially stronger than monotone circuits.
We show that the size of any circuit of negation width w computing f is roughly at least the minimum size of a monotone circuit computing f divided by K=min{w^m,m^w}, where m is the maximum length of a prime implicant of f. We also show that the depth of any circuit of negation width w computing f is roughly at least the minimum depth of a monotone circuit computing f minus log K. Finally, we show that formulas of bounded negation width can be balanced to achieve a logarithmic (in their size) depth without increasing their negation width.
Cite as
Stasys Jukna and Andrzej Lingas. Lower Bounds for DeMorgan Circuits of Bounded Negation Width. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{jukna_et_al:LIPIcs.STACS.2019.41,
author = {Jukna, Stasys and Lingas, Andrzej},
title = {{Lower Bounds for DeMorgan Circuits of Bounded Negation Width}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {41:1--41:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.41},
URN = {urn:nbn:de:0030-drops-102801},
doi = {10.4230/LIPIcs.STACS.2019.41},
annote = {Keywords: Boolean circuits, monotone circuits, lower bounds}
}
Document
Depth First Search in the Semi-streaming Model
Abstract
Depth first search (DFS) tree is a fundamental data structure for solving various graph problems. The classical algorithm for building a DFS tree requires O(m+n) time for a given undirected graph G having n vertices and m edges. In the streaming model, an algorithm is allowed several passes (preferably single) over the input graph having a restriction on the size of local space used.
Now, a DFS tree of a graph can be trivially computed using a single pass if O(m) space is allowed. In the semi-streaming model allowing O(n) space, it can be computed in O(n) passes over the input stream, where each pass adds one vertex to the DFS tree. However, it remains an open problem to compute a DFS tree using o(n) passes using o(m) space even in any relaxed streaming environment.
We present the first semi-streaming algorithms that compute a DFS tree of an undirected graph in o(n) passes using o(m) space. We first describe an extremely simple algorithm that requires at most ceil[n/k] passes to compute a DFS tree using O(nk) space, where k is any positive integer. For example using k=sqrt{n}, we can compute a DFS tree in sqrt{n} passes using O(n sqrt{n}) space. We then improve this algorithm by using more involved techniques to reduce the number of passes to ceil[h/k] under similar space constraints, where h is the height of the computed DFS tree. In particular, this algorithm improves the bounds for the case where the computed DFS tree is shallow (having o(n) height). Moreover, this algorithm is presented in form of a framework that allows the flexibility of using any algorithm to maintain a DFS tree of a stored sparser subgraph as a black box, which may be of an independent interest. Both these algorithms essentially demonstrate the existence of a trade-off between the space and number of passes required for computing a DFS tree. Furthermore, we evaluate these algorithms experimentally which reveals their exceptional performance in practice. For both random and real graphs, they require merely a few passes even when allowed just O(n) space.
Cite as
Shahbaz Khan and Shashank K. Mehta. Depth First Search in the Semi-streaming Model. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 42:1-42:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{khan_et_al:LIPIcs.STACS.2019.42,
author = {Khan, Shahbaz and K. Mehta, Shashank},
title = {{Depth First Search in the Semi-streaming Model}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {42:1--42:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.42},
URN = {urn:nbn:de:0030-drops-102818},
doi = {10.4230/LIPIcs.STACS.2019.42},
annote = {Keywords: Depth First Search, DFS, Semi-Streaming, Streaming, Algorithm}
}
Document
On Finite Monoids over Nonnegative Integer Matrices and Short Killing Words
Abstract
Let n be a natural number and M a set of n x n-matrices over the nonnegative integers such that M generates a finite multiplicative monoid. We show that if the zero matrix 0 is a product of matrices in M, then there are M_1, ..., M_{n^5} in M with M_1 *s M_{n^5} = 0. This result has applications in automata theory and the theory of codes. Specifically, if X subset Sigma^* is a finite incomplete code, then there exists a word w in Sigma^* of length polynomial in sum_{x in X} |x| such that w is not a factor of any word in X^*. This proves a weak version of Restivo’s conjecture.
Cite as
Stefan Kiefer and Corto Mascle. On Finite Monoids over Nonnegative Integer Matrices and Short Killing Words. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 43:1-43:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{kiefer_et_al:LIPIcs.STACS.2019.43,
author = {Kiefer, Stefan and Mascle, Corto},
title = {{On Finite Monoids over Nonnegative Integer Matrices and Short Killing Words}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {43:1--43:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.43},
URN = {urn:nbn:de:0030-drops-102823},
doi = {10.4230/LIPIcs.STACS.2019.43},
annote = {Keywords: matrix semigroups, unambiguous automata, codes, Restivo’s conjecture}
}
Document
Tight Complexity Lower Bounds for Integer Linear Programming with Few Constraints
Abstract
We consider the standard ILP Feasibility problem: given an integer linear program of the form {Ax = b, x >= 0}, where A is an integer matrix with k rows and l columns, x is a vector of l variables, and b is a vector of k integers, we ask whether there exists x in N^l that satisfies Ax = b. Each row of A specifies one linear constraint on x; our goal is to study the complexity of ILP Feasibility when both k, the number of constraints, and |A|_infty, the largest absolute value of an entry in A, are small.
Papadimitriou [Christos H. Papadimitriou, 1981] was the first to give a fixed-parameter algorithm for ILP Feasibility under parameterization by the number of constraints that runs in time ((|A |_infty + |b|_infty) * k)^O(k^2). This was very recently improved by Eisenbrand and Weismantel [Friedrich Eisenbrand and Robert Weismantel, 2018], who used the Steinitz lemma to design an algorithm with running time (k |A|_infty)^{O(k)}* |b|_infty^2, which was subsequently improved by Jansen and Rohwedder [Klaus Jansen and Lars Rohwedder, 2019] to O(k |A |_infty)^k* log |b|_infty. We prove that for {0,1}-matrices A, the running time of the algorithm of Eisenbrand and Weismantel is probably optimal: an algorithm with running time 2^{o(k log k)}* (l+|{b}|_infty)^{o(k)} would contradict the Exponential Time Hypothesis (ETH). This improves previous non-tight lower bounds of Fomin et al. [Fedor V. Fomin et al., 2018].
We then consider integer linear programs that may have many constraints, but they need to be structured in a "shallow" way. Precisely, we consider the parameter {dual treedepth} of the matrix A, denoted td_D(A), which is the treedepth of the graph over the rows of A, where two rows are adjacent if in some column they simultaneously contain a non-zero entry. It was recently shown by Koutecký et al. [Martin Koutecký et al., 2018] that {ILP Feasibility} can be solved in time |A |_infty^{2^O(td_D(A))} * (k+l+log |b|_infty)^O(1). We present a streamlined proof of this fact and prove that, again, this running time is probably optimal: even assuming that all entries of A and {b} are in {-1,0,1}, the existence of an algorithm with running time 2^{2^o(td_D(A))} * (k+l)^O(1) would contradict the ETH.
Cite as
Dušan Knop, Michał Pilipczuk, and Marcin Wrochna. Tight Complexity Lower Bounds for Integer Linear Programming with Few Constraints. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 44:1-44:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{knop_et_al:LIPIcs.STACS.2019.44,
author = {Knop, Du\v{s}an and Pilipczuk, Micha{\l} and Wrochna, Marcin},
title = {{Tight Complexity Lower Bounds for Integer Linear Programming with Few Constraints}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {44:1--44:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.44},
URN = {urn:nbn:de:0030-drops-102831},
doi = {10.4230/LIPIcs.STACS.2019.44},
annote = {Keywords: integer linear programming, fixed-parameter tractability, ETH}
}
Document
The Set Cover Conjecture and Subgraph Isomorphism with a Tree Pattern
Abstract
In the Set Cover problem, the input is a ground set of n elements and a collection of m sets, and the goal is to find the smallest sub-collection of sets whose union is the entire ground set. The fastest algorithm known runs in time O(mn2^n) [Fomin et al., WG 2004], and the Set Cover Conjecture (SeCoCo) [Cygan et al., TALG 2016] asserts that for every fixed epsilon>0, no algorithm can solve Set Cover in time 2^{(1-epsilon)n} poly(m), even if set sizes are bounded by Delta=Delta(epsilon). We show strong connections between this problem and kTree, a special case of Subgraph Isomorphism where the input is an n-node graph G and a k-node tree T, and the goal is to determine whether G has a subgraph isomorphic to T.
First, we propose a weaker conjecture Log-SeCoCo, that allows input sets of size Delta=O(1/epsilon * log n), and show that an algorithm breaking Log-SeCoCo would imply a faster algorithm than the currently known 2^n poly(n)-time algorithm [Koutis and Williams, TALG 2016] for Directed nTree, which is kTree with k=n and arbitrary directions to the edges of G and T. This would also improve the running time for Directed Hamiltonicity, for which no algorithm significantly faster than 2^n poly(n) is known despite extensive research.
Second, we prove that if p-Partial Cover, a parameterized version of Set Cover that requires covering at least p elements, cannot be solved significantly faster than 2^n poly(m) (an assumption even weaker than Log-SeCoCo) then kTree cannot be computed significantly faster than 2^k poly(n), the running time of the Koutis and Williams' algorithm.
Cite as
Robert Krauthgamer and Ohad Trabelsi. The Set Cover Conjecture and Subgraph Isomorphism with a Tree Pattern. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 45:1-45:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{krauthgamer_et_al:LIPIcs.STACS.2019.45,
author = {Krauthgamer, Robert and Trabelsi, Ohad},
title = {{The Set Cover Conjecture and Subgraph Isomorphism with a Tree Pattern}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {45:1--45:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.45},
URN = {urn:nbn:de:0030-drops-102840},
doi = {10.4230/LIPIcs.STACS.2019.45},
annote = {Keywords: Conditional lower bounds, Hardness in P, Set Cover Conjecture, Subgraph Isomorphism}
}
Document
Algorithmic Properties of Sparse Digraphs
Abstract
The notions of bounded expansion [Nešetřil and Ossona de Mendez, 2008] and nowhere denseness [Nešetřil and Ossona de Mendez, 2011], introduced by Nešetřil and Ossona de Mendez as structural measures for undirected graphs, have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs, introduced by Kreutzer and Tazari [Kreutzer and Tazari, 2012]. The classes of directed graphs having those properties are very general classes of sparse directed graphs, as they include, on one hand, all classes of directed graphs whose underlying undirected class has bounded expansion, such as planar, bounded-genus, and H-minor-free graphs, and on the other hand, they also contain classes whose underlying undirected class is not even nowhere dense. We show that many of the algorithmic tools that were developed for undirected bounded expansion classes can, with some care, also be applied in their directed counterparts, and thereby we highlight a rich algorithmic structure theory of directed bounded expansion and nowhere crownful classes.
Cite as
Stephan Kreutzer, Irene Muzi, Patrice Ossona de Mendez, Roman Rabinovich, and Sebastian Siebertz. Algorithmic Properties of Sparse Digraphs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{kreutzer_et_al:LIPIcs.STACS.2019.46,
author = {Kreutzer, Stephan and Muzi, Irene and Ossona de Mendez, Patrice and Rabinovich, Roman and Siebertz, Sebastian},
title = {{Algorithmic Properties of Sparse Digraphs}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {46:1--46:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.46},
URN = {urn:nbn:de:0030-drops-102859},
doi = {10.4230/LIPIcs.STACS.2019.46},
annote = {Keywords: Directed graphs, graph algorithms, parameterized complexity, approximation}
}
Document
Tree Automata with Global Constraints for Infinite Trees
Abstract
We study an extension of tree automata on infinite trees with global equality and disequality constraints. These constraints can enforce that all subtrees for which in the accepting run a state q is reached (at the root of that subtree) are identical, or that these trees differ from the subtrees at which a state q' is reached. We consider the closure properties of this model and its decision problems. While the emptiness problem for the general model remains open, we show the decidability of the emptiness problem for the case that the given automaton only uses equality constraints.
Cite as
Patrick Landwehr and Christof Löding. Tree Automata with Global Constraints for Infinite Trees. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 47:1-47:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{landwehr_et_al:LIPIcs.STACS.2019.47,
author = {Landwehr, Patrick and L\"{o}ding, Christof},
title = {{Tree Automata with Global Constraints for Infinite Trees}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {47:1--47:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.47},
URN = {urn:nbn:de:0030-drops-102863},
doi = {10.4230/LIPIcs.STACS.2019.47},
annote = {Keywords: Tree automata, infinite trees, global constraints}
}
Document
Constructive Discrepancy Minimization with Hereditary L2 Guarantees
Abstract
In discrepancy minimization problems, we are given a family of sets S = {S_1,...,S_m}, with each S_i in S a subset of some universe U = {u_1,...,u_n} of n elements. The goal is to find a coloring chi : U -> {-1,+1} of the elements of U such that each set S in S is colored as evenly as possible. Two classic measures of discrepancy are l_infty-discrepancy defined as disc_infty(S,chi):=max_{S in S} | sum_{u_i in S} chi(u_i) | and l_2-discrepancy defined as disc_2(S,chi):=sqrt{(1/|S|) sum_{S in S} (sum_{u_i in S} chi(u_i))^2}. Breakthrough work by Bansal [FOCS'10] gave a polynomial time algorithm, based on rounding an SDP, for finding a coloring chi such that disc_infty(S,chi) = O(lg n * herdisc_infty(S)) where herdisc_infty(S) is the hereditary l_infty-discrepancy of S. We complement his work by giving a clean and simple O((m+n)n^2) time algorithm for finding a coloring chi such disc_2(S,chi) = O(sqrt{lg n} * herdisc_2(S)) where herdisc_2(S) is the hereditary l_2-discrepancy of S. Interestingly, our algorithm avoids solving an SDP and instead relies simply on computing eigendecompositions of matrices. To prove that our algorithm has the claimed guarantees, we also prove new inequalities relating both herdisc_infty and herdisc_2 to the eigenvalues of the incidence matrix corresponding to S. Our inequalities improve over previous work by Chazelle and Lvov [SCG'00] and by Matousek, Nikolov and Talwar [SODA'15+SCG'15]. We believe these inequalities are of independent interest as powerful tools for proving hereditary discrepancy lower bounds. Finally, we also implement our algorithm and show that it far outperforms random sampling of colorings in practice. Moreover, the algorithm finishes in a reasonable amount of time on matrices of sizes up to 10000 x 10000.
Cite as
Kasper Green Larsen. Constructive Discrepancy Minimization with Hereditary L2 Guarantees. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 48:1-48:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{larsen:LIPIcs.STACS.2019.48,
author = {Larsen, Kasper Green},
title = {{Constructive Discrepancy Minimization with Hereditary L2 Guarantees}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {48:1--48:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.48},
URN = {urn:nbn:de:0030-drops-102878},
doi = {10.4230/LIPIcs.STACS.2019.48},
annote = {Keywords: Discrepancy, Hereditary Discrepancy, Combinatorics, Computational Geometry}
}
Document
Quantum Advantage for the LOCAL Model in Distributed Computing
Abstract
There are two central models considered in (fault-free synchronous) distributed computing: the CONGEST model, in which communication channels have limited bandwidth, and the LOCAL model, in which communication channels have unlimited bandwidth. Very recently, Le Gall and Magniez (PODC 2018) showed the superiority of quantum distributed computing over classical distributed computing in the CONGEST model. In this work we show the superiority of quantum distributed computing in the LOCAL model: we exhibit two computational tasks that can be solved in a constant number of rounds in the quantum setting but require Omega(n) rounds in the classical (randomized) setting, where n denotes the size of the network.
Cite as
François Le Gall, Harumichi Nishimura, and Ansis Rosmanis. Quantum Advantage for the LOCAL Model in Distributed Computing. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{legall_et_al:LIPIcs.STACS.2019.49,
author = {Le Gall, Fran\c{c}ois and Nishimura, Harumichi and Rosmanis, Ansis},
title = {{Quantum Advantage for the LOCAL Model in Distributed Computing}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {49:1--49:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.49},
URN = {urn:nbn:de:0030-drops-102887},
doi = {10.4230/LIPIcs.STACS.2019.49},
annote = {Keywords: Quantum computing, distributed computing, LOCAL model}
}
Document
Lifting Theorems for Equality
Abstract
We show a deterministic simulation (or lifting) theorem for composed problems f o Eq_n where the inner function (the gadget) is Equality on n bits. When f is a total function on p bits, it is easy to show via a rank argument that the communication complexity of f o Eq_n is Omega(deg(f) * n). However, there is a surprising counter-example of a partial function f on p bits, such that any completion f' of f has deg(f') = Omega(p), and yet f o Eq_n has communication complexity O(n). Nonetheless, we are able to show that the communication complexity of f o Eq_n is at least D(f) * n for a complexity measure D(f) which is closely related to the AND-query complexity of f and is lower-bounded by the logarithm of the leaf complexity of f. As a corollary, we also obtain lifting theorems for the set-disjointness gadget, and a lifting theorem in the context of parity decision-trees, for the NOR gadget.
As an application, we prove a tight lower-bound for the deterministic communication complexity of the communication problem, where Alice and Bob are each given p-many n-bit strings, with the promise that either all of the strings are distinct, or all-but-one of the strings are distinct, and they wish to know which is the case. We show that the complexity of this problem is Theta(p * n).
Cite as
Bruno Loff and Sagnik Mukhopadhyay. Lifting Theorems for Equality. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 50:1-50:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{loff_et_al:LIPIcs.STACS.2019.50,
author = {Loff, Bruno and Mukhopadhyay, Sagnik},
title = {{Lifting Theorems for Equality}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {50:1--50:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.50},
URN = {urn:nbn:de:0030-drops-102892},
doi = {10.4230/LIPIcs.STACS.2019.50},
annote = {Keywords: Communication complexity, Query complexity, Simulation theorem, Equality function}
}
Document
Car-Sharing on a Star Network: On-Line Scheduling with k Servers
Abstract
We study an on-line scheduling problem that is motivated by applications such as car-sharing for trips between an airport and a group of hotels. Users submit ride requests, and the scheduler aims to accept requests of maximum total profit using k servers (cars). Each ride request specifies the pick-up time, the pick-up location, and the drop-off location, where one of the two locations must be the airport. A request must be submitted a fixed amount of time before the pick-up time. The scheduler has to decide whether or not to accept a request immediately at the time when the request is submitted (booking time). In the unit travel time variant, the travel time between the airport and any hotel is a fixed value t. We give a 2-competitive algorithm for the case in which the booking interval (pick-up time minus booking time) is at least t and the number of servers is even. In the arbitrary travel time variant, the travel time between the airport and a hotel may have arbitrary length between t and L t for some L >= 1. We give an algorithm with competitive ratio O(log L) if the number of servers is at least ceil[log L]. For both variants, we prove matching lower bounds on the competitive ratio of any deterministic on-line algorithm.
Cite as
Kelin Luo, Thomas Erlebach, and Yinfeng Xu. Car-Sharing on a Star Network: On-Line Scheduling with k Servers. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 51:1-51:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{luo_et_al:LIPIcs.STACS.2019.51,
author = {Luo, Kelin and Erlebach, Thomas and Xu, Yinfeng},
title = {{Car-Sharing on a Star Network: On-Line Scheduling with k Servers}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {51:1--51:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.51},
URN = {urn:nbn:de:0030-drops-102907},
doi = {10.4230/LIPIcs.STACS.2019.51},
annote = {Keywords: Car-Sharing System, On-Line Scheduling, Competitive Analysis, Star Network}
}
Document
Beyond Boolean Surjective VCSPs
Abstract
Fulla, Uppman, and Živný [ACM ToCT'18] established a dichotomy theorem for Boolean surjective general-valued constraint satisfaction problems (VCSPs), i.e., VCSPs on two-element domains in which both labels have to be used in a solution. This result, in addition to identifying the complexity frontier, features the discovery of a new non-trivial tractable case (called EDS) that does not appear in the non-surjective setting.
In this work, we go beyond Boolean domains. As our main result, we introduce a generalisation of EDS to arbitrary finite domains called SEDS (similar to EDS) and establish a conditional complexity classification of SEDS VCSPs based on a reduction to smaller domains. This gives a complete classification of SEDS VCSPs on three-element domains. The basis of our tractability result is a natural generalisation of the Min-Cut problem, in which only solutions of certain size (given by a lower and upper bound) are permitted. We show that all near-optimal solutions to this problem can be enumerated in polynomial time, which might be of independent interest.
Cite as
Gregor Matl and Stanislav Živný. Beyond Boolean Surjective VCSPs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{matl_et_al:LIPIcs.STACS.2019.52,
author = {Matl, Gregor and \v{Z}ivn\'{y}, Stanislav},
title = {{Beyond Boolean Surjective VCSPs}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {52:1--52:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.52},
URN = {urn:nbn:de:0030-drops-102911},
doi = {10.4230/LIPIcs.STACS.2019.52},
annote = {Keywords: constraint satisfaction problems, valued constraint satisfaction, surjective constraint satisfaction, graph cuts}
}
Document
The Containment Problem for Unambiguous Register Automata
Abstract
We investigate the complexity of the containment problem "Does L(A)subseteq L(B) hold?", where B is an unambiguous register automaton and A is an arbitrary register automaton. We prove that the problem is decidable and give upper bounds on the computational complexity in the general case, and when B is restricted to have a fixed number of registers.
Cite as
Antoine Mottet and Karin Quaas. The Containment Problem for Unambiguous Register Automata. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 53:1-53:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{mottet_et_al:LIPIcs.STACS.2019.53,
author = {Mottet, Antoine and Quaas, Karin},
title = {{The Containment Problem for Unambiguous Register Automata}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {53:1--53:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.53},
URN = {urn:nbn:de:0030-drops-102926},
doi = {10.4230/LIPIcs.STACS.2019.53},
annote = {Keywords: Data words, Register automata, Unambiguous Automata, Containment Problem, Language Inclusion Problem}
}
Document
Stabilization Time in Weighted Minority Processes
Abstract
A minority process in a weighted graph is a dynamically changing coloring. Each node repeatedly changes its color in order to minimize the sum of weighted conflicts with its neighbors. We study the number of steps until such a process stabilizes. Our main contribution is an exponential lower bound on stabilization time. We first present a construction showing this bound in the adversarial sequential model, and then we show how to extend the construction to establish the same bound in the benevolent sequential model, as well as in any reasonable concurrent model. Furthermore, we show that the stabilization time of our construction remains exponential even for very strict switching conditions, namely, if a node only changes color when almost all (i.e., any specific fraction) of its neighbors have the same color. Our lower bound works in a wide range of settings, both for node-weighted and edge-weighted graphs, or if we restrict minority processes to the class of sparse graphs.
Cite as
Pál András Papp and Roger Wattenhofer. Stabilization Time in Weighted Minority Processes. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 54:1-54:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{papp_et_al:LIPIcs.STACS.2019.54,
author = {Papp, P\'{a}l Andr\'{a}s and Wattenhofer, Roger},
title = {{Stabilization Time in Weighted Minority Processes}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {54:1--54:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.54},
URN = {urn:nbn:de:0030-drops-102938},
doi = {10.4230/LIPIcs.STACS.2019.54},
annote = {Keywords: Minority process, Benevolent model}
}
Document
Finite Sequentiality of Unambiguous Max-Plus Tree Automata
Abstract
We show the decidability of the finite sequentiality problem for unambiguous max-plus tree automata. A max-plus tree automaton is called unambiguous if there is at most one accepting run on every tree. The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton.
Cite as
Erik Paul. Finite Sequentiality of Unambiguous Max-Plus Tree Automata. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{paul:LIPIcs.STACS.2019.55,
author = {Paul, Erik},
title = {{Finite Sequentiality of Unambiguous Max-Plus Tree Automata}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {55:1--55:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.55},
URN = {urn:nbn:de:0030-drops-102946},
doi = {10.4230/LIPIcs.STACS.2019.55},
annote = {Keywords: Weighted Tree Automata, Max-Plus Tree Automata, Finite Sequentiality, Decidability, Ambiguity}
}
Document
Paging with Dynamic Memory Capacity
Abstract
We study a generalization of the classic paging problem that allows the amount of available memory to vary over time - capturing a fundamental property of many modern computing realities, from cloud computing to multi-core and energy-optimized processors.
It turns out that good performance in the "classic" case provides no performance guarantees when memory capacity fluctuates: roughly speaking, moving from static to dynamic capacity can mean the difference between optimality within a factor 2 in space and time, and suboptimality by an arbitrarily large factor. More precisely, adopting the competitive analysis framework, we show that some online paging algorithms, despite having an optimal (h,k)-competitive ratio when capacity remains constant, are not (3,k)-competitive for any arbitrarily large k in the presence of minimal capacity fluctuations.
In this light it is surprising that several classic paging algorithms perform remarkably well even if memory capacity changes adversarially - in fact, even without taking those changes into explicit account! In particular, we prove that LFD still achieves the minimum number of faults, and that several classic online algorithms such as LRU have a "dynamic" (h,k)-competitive ratio that is the best one can achieve without knowledge of future page requests, even if one had perfect knowledge of future capacity fluctuations. Thus, with careful management, knowing/predicting future memory resources appears far less crucial to performance than knowing/predicting future data accesses.
We characterize the optimal "dynamic" (h,k)-competitive ratio exactly, and show it has a somewhat complex expression that is almost but not quite equal to the "classic" ratio k/(k-h+1), thus proving a strict if minuscule separation between online paging performance achievable in the presence or absence of capacity fluctuations.
Cite as
Enoch Peserico. Paging with Dynamic Memory Capacity. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 56:1-56:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{peserico:LIPIcs.STACS.2019.56,
author = {Peserico, Enoch},
title = {{Paging with Dynamic Memory Capacity}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {56:1--56:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.56},
URN = {urn:nbn:de:0030-drops-102951},
doi = {10.4230/LIPIcs.STACS.2019.56},
annote = {Keywords: paging, cache, adaptive, elastic, online, competitive, virtual, energy}
}
Document
Random Noise Increases Kolmogorov Complexity and Hausdorff Dimension
Abstract
Consider a bit string x of length n and Kolmogorov complexity alpha n (for some alpha<1). It is always possible to increase the complexity of x by changing a small fraction of bits in x [Harry Buhrman et al., 2005]. What happens with the complexity of x when we randomly change each bit independently with some probability tau? We prove that a linear increase in complexity happens with high probability, but this increase is smaller than in the case of arbitrary change considered in [Harry Buhrman et al., 2005]. The amount of the increase depends on x (strings of the same complexity could behave differently). We give exact lower and upper bounds for this increase (with o(n) precision).
The same technique is used to prove the results about the (effective Hausdorff) dimension of infinite sequences. We show that random change increases the dimension with probability 1, and provide an optimal lower bound for the dimension of the changed sequence. We also improve a result from [Noam Greenberg et al., 2018] and show that for every sequence omega of dimension alpha there exists a strongly alpha-random sequence omega' such that the Besicovitch distance between omega and omega' is 0.
The proofs use the combinatorial and probabilistic reformulations of complexity statements and the technique that goes back to Ahlswede, Gács and Körner [Ahlswede et al., 1976].
Cite as
Gleb Posobin and Alexander Shen. Random Noise Increases Kolmogorov Complexity and Hausdorff Dimension. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 57:1-57:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{posobin_et_al:LIPIcs.STACS.2019.57,
author = {Posobin, Gleb and Shen, Alexander},
title = {{Random Noise Increases Kolmogorov Complexity and Hausdorff Dimension}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {57:1--57:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.57},
URN = {urn:nbn:de:0030-drops-102969},
doi = {10.4230/LIPIcs.STACS.2019.57},
annote = {Keywords: Kolmogorov complexity, effective Hausdorff dimension, random noise}
}
Document
A Unified Approach to Tail Estimates for Randomized Incremental Construction
Abstract
By combining several interesting applications of random sampling in geometric algorithms like point location, linear programming, segment intersections, binary space partitioning, Clarkson and Shor [Kenneth L. Clarkson and Peter W. Shor, 1989] developed a general framework of randomized incremental construction (RIC ). The basic idea is to add objects in a random order and show that this approach yields efficient/optimal bounds on expected running time. Even quicksort can be viewed as a special case of this paradigm. However, unlike quicksort, for most of these problems, sharper tail estimates on their running times are not known. Barring some promising attempts in [Kurt Mehlhorn et al., 1993; Kenneth L. Clarkson et al., 1992; Raimund Seidel, 1991], the general question remains unresolved.
In this paper we present a general technique to obtain tail estimates for RIC and and provide applications to some fundamental problems like Delaunay triangulations and construction of Visibility maps of intersecting line segments. The main result of the paper is derived from a new and careful application of Freedman’s [David Freedman, 1975] inequality for Martingale concentration that overcomes the bottleneck of the better known Azuma-Hoeffding inequality. Further, we explore instances, where an RIC based algorithm may not have inverse polynomial tail estimates. In particular, we show that the RIC time bounds for trapezoidal map can encounter a running time of Omega (n log n log log n) with probability exceeding 1/(sqrt{n)}. This rules out inverse polynomial concentration bounds within a constant factor of the O(n log n) expected running time.
Cite as
Sandeep Sen. A Unified Approach to Tail Estimates for Randomized Incremental Construction. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 58:1-58:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{sen:LIPIcs.STACS.2019.58,
author = {Sen, Sandeep},
title = {{A Unified Approach to Tail Estimates for Randomized Incremental Construction}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {58:1--58:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.58},
URN = {urn:nbn:de:0030-drops-102977},
doi = {10.4230/LIPIcs.STACS.2019.58},
annote = {Keywords: ric, tail estimates, martingale, lower bound}
}
Document
A ZPP^NP[1] Lifting Theorem
Abstract
The complexity class ZPP^{NP[1]} (corresponding to zero-error randomized algorithms with access to one NP oracle query) is known to have a number of curious properties. We further explore this class in the settings of time complexity, query complexity, and communication complexity.
- For starters, we provide a new characterization: ZPP^{NP[1]} equals the restriction of BPP^{NP[1]} where the algorithm is only allowed to err when it forgoes the opportunity to make an NP oracle query.
- Using the above characterization, we prove a query-to-communication lifting theorem, which translates any ZPP^{NP[1]} decision tree lower bound for a function f into a ZPP^{NP[1]} communication lower bound for a two-party version of f.
- As an application, we use the above lifting theorem to prove that the ZPP^{NP[1]} communication lower bound technique introduced by Göös, Pitassi, and Watson (ICALP 2016) is not tight. We also provide a "primal" characterization of this lower bound technique as a complexity class.
Cite as
Thomas Watson. A ZPP^NP[1] Lifting Theorem. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 59:1-59:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
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@InProceedings{watson:LIPIcs.STACS.2019.59,
author = {Watson, Thomas},
title = {{A ZPP^NP\lbrack1\rbrack Lifting Theorem}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {59:1--59:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-100-9},
ISSN = {1868-8969},
year = {2019},
volume = {126},
editor = {Niedermeier, Rolf and Paul, Christophe},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.59},
URN = {urn:nbn:de:0030-drops-102989},
doi = {10.4230/LIPIcs.STACS.2019.59},
annote = {Keywords: Query complexity, communication complexity, lifting}
}