Volume
LIPIcs, Volume 117
43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Mathematical Foundations of Computer Science (MFCS)
Event
MFCS 2018, August 27-31, 2018, Liverpool, GBEditors
Publication Details
- published at: 2018-08-27
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-086-6
- DBLP: db/conf/mfcs/mfcs2018
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Complete Volume
LIPIcs, Volume 117, MFCS'18, Complete Volume
Abstract
LIPIcs, Volume 117, MFCS'18, Complete Volume
Cite as
43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@Proceedings{potapov_et_al:LIPIcs.MFCS.2018,
title = {{LIPIcs, Volume 117, MFCS'18, Complete Volume}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018},
URN = {urn:nbn:de:0030-drops-97459},
doi = {10.4230/LIPIcs.MFCS.2018},
annote = {Keywords: Theory of computation}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{potapov_et_al:LIPIcs.MFCS.2018.0,
author = {Potapov, Igor and Spirakis, Paul and Worrell, James},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {0:i--0:xx},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.0},
URN = {urn:nbn:de:0030-drops-95824},
doi = {10.4230/LIPIcs.MFCS.2018.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Consensus Strings with Small Maximum Distance and Small Distance Sum
Abstract
The parameterised complexity of consensus string problems (Closest String, Closest Substring, Closest String with Outliers) is investigated in a more general setting, i. e., with a bound on the maximum Hamming distance and a bound on the sum of Hamming distances between solution and input strings. We completely settle the parameterised complexity of these generalised variants of Closest String and Closest Substring, and partly for Closest String with Outliers; in addition, we answer some open questions from the literature regarding the classical problem variants with only one distance bound. Finally, we investigate the question of polynomial kernels and respective lower bounds.
Cite as
Laurent Bulteau and Markus L. Schmid. Consensus Strings with Small Maximum Distance and Small Distance Sum. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{bulteau_et_al:LIPIcs.MFCS.2018.1,
author = {Bulteau, Laurent and Schmid, Markus L.},
title = {{Consensus Strings with Small Maximum Distance and Small Distance Sum}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {1:1--1:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.1},
URN = {urn:nbn:de:0030-drops-95834},
doi = {10.4230/LIPIcs.MFCS.2018.1},
annote = {Keywords: Consensus String Problems, Closest String, Closest Substring, Parameterised Complexity, Kernelisation}
}
Document
Plain Stopping Time and Conditional Complexities Revisited
Abstract
In this paper we analyze the notion of "stopping time complexity", the amount of information needed to specify when to stop while reading an infinite sequence. This notion was introduced by Vovk and Pavlovic [Vovk and Pavlovic, 2016]. It turns out that plain stopping time complexity of a binary string x could be equivalently defined as (a) the minimal plain complexity of a Turing machine that stops after reading x on a one-directional input tape; (b) the minimal plain complexity of an algorithm that enumerates a prefix-free set containing x; (c) the conditional complexity C(x|x*) where x in the condition is understood as a prefix of an infinite binary sequence while the first x is understood as a terminated binary string; (d) as a minimal upper semicomputable function K such that each binary sequence has at most 2^n prefixes z such that K(z)<n; (e) as maxC^X(x) where C^X(z) is plain Kolmogorov complexity of z relative to oracle X and the maximum is taken over all extensions X of x.
We also show that some of these equivalent definitions become non-equivalent in the more general setting where the condition y and the object x may differ, and answer an open question from Chernov, Hutter and Schmidhuber [Alexey V. Chernov et al., 2007].
Cite as
Mikhail Andreev, Gleb Posobin, and Alexander Shen. Plain Stopping Time and Conditional Complexities Revisited. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{andreev_et_al:LIPIcs.MFCS.2018.2,
author = {Andreev, Mikhail and Posobin, Gleb and Shen, Alexander},
title = {{Plain Stopping Time and Conditional Complexities Revisited}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {2:1--2:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.2},
URN = {urn:nbn:de:0030-drops-95842},
doi = {10.4230/LIPIcs.MFCS.2018.2},
annote = {Keywords: Kolmogorov complexity, stopping time complexity, structured conditional complexity, algorithmic information theory}
}
Document
Error-Tolerant Non-Adaptive Learning of a Hidden Hypergraph
Abstract
We consider the problem of learning the hypergraph using edge-detecting queries. In this model, the learner is allowed to query whether a set of vertices includes an edge from a hidden hypergraph. Except a few, all previous algorithms assume that a query's result is always correct. In this paper we study the problem of learning a hypergraph where alpha -fraction of the queries are incorrect. The main contribution of this paper is generalizing the well-known structure CFF (Cover Free Family) to be Dense (we will call it DCFF - Dense Cover Free Family) while presenting three different constructions for DCFF. Later, we use these constructions wisely to give a polynomial time non-adaptive learning algorithm for a hypergraph problem with at most alpha-fracion incorrect queries. The hypergraph problem is also known as both monotone DNF learning problem, and complexes group testing problem.
Cite as
Hasan Abasi. Error-Tolerant Non-Adaptive Learning of a Hidden Hypergraph. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{abasi:LIPIcs.MFCS.2018.3,
author = {Abasi, Hasan},
title = {{Error-Tolerant Non-Adaptive Learning of a Hidden Hypergraph}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {3:1--3:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.3},
URN = {urn:nbn:de:0030-drops-95854},
doi = {10.4230/LIPIcs.MFCS.2018.3},
annote = {Keywords: Error Tolerant Algorithm, Hidden Hypergraph, Montone DNF, Group Testing, Non-Adaptive Learning}
}
Document
From Expanders to Hitting Distributions and Simulation Theorems
Abstract
In this paper we explore hitting distributions, a notion that arose recently in the context of deterministic "query-to-communication" simulation theorems. We show that any expander in which any two distinct vertices have at most one common neighbor can be transformed into a gadget possessing good hitting distributions. We demonstrate that this result is applicable to affine plane expanders and to Lubotzky-Phillips-Sarnak construction of Ramanujan graphs . In particular, from affine plane expanders we extract a gadget achieving the best known trade-off between the arity of outer function and the size of gadget. More specifically, when this gadget has k bits on input, it admits a simulation theorem for all outer function of arity roughly 2^(k/2) or less (the same was also known for k-bit Inner Product). In addition we show that, unlike Inner Product, underlying hitting distributions in our new gadget are "polynomial-time listable" in the sense that their supports can be written down in time 2^O(k), i.e. in time polynomial in size of gadget's matrix.
We also obtain two results showing that with current technique no better trade-off between the arity of outer function and the size of gadget can be achieved. Namely, we observe that no gadget can have hitting distributions with significantly better parameters than Inner Product or our new affine plane gadget. We also show that Thickness Lemma, a place which causes restrictions on the arity of outer functions in proofs of simulation theorems, is unimprovable.
Cite as
Alexander Kozachinskiy. From Expanders to Hitting Distributions and Simulation Theorems. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{kozachinskiy:LIPIcs.MFCS.2018.4,
author = {Kozachinskiy, Alexander},
title = {{From Expanders to Hitting Distributions and Simulation Theorems}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {4:1--4:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.4},
URN = {urn:nbn:de:0030-drops-95863},
doi = {10.4230/LIPIcs.MFCS.2018.4},
annote = {Keywords: simulation theorems, hitting distributions, expanders}
}
Document
Balance Problems for Integer Circuits
Abstract
We investigate the computational complexity of balance problems for {-,*}-circuits computing finite sets of natural numbers. These problems naturally build on problems for integer expressions and integer circuits studied by Stockmeyer and Meyer (1973), McKenzie and Wagner (2007), and Glaßer et al. (2010).
Our work shows that the balance problem for {-,*}-circuits is undecidable which is the first natural problem for integer circuits or related constraint satisfaction problems that admits only one arithmetic operation and is proven to be undecidable.
Starting from this result we precisely characterize the complexity of balance problems for proper subsets of {-,*}. These problems turn out to be complete for one of the classes L, NL, and NP.
Cite as
Titus Dose. Balance Problems for Integer Circuits. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{dose:LIPIcs.MFCS.2018.5,
author = {Dose, Titus},
title = {{Balance Problems for Integer Circuits}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {5:1--5:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.5},
URN = {urn:nbn:de:0030-drops-95874},
doi = {10.4230/LIPIcs.MFCS.2018.5},
annote = {Keywords: computational complexity, integer expressions, integer circuits}
}
Document
On Hadamard Series and Rotating Q-Automata
Abstract
In this paper, we study rotating Q-automata, which are (memoryless) automata with weights in Q, that can read the input tape from left to right several times. We show that the series realized by valid rotating Q-automata are Q-Hadamard series (which are the closure of Q-rational series by pointwise inverse), and that every Q-Hadamard series can be realized by such an automaton. We prove that, although validity of rotating Q-automata is undecidable, the equivalence problem is decidable on rotating Q-automata. Finally, we prove that every valid two-way Q-automaton admits an equivalent rotating Q-automaton. The conversion, which is effective, implies the decidability of equivalence of two-way Q-automata.
Cite as
Louis-Marie Dando and Sylvain Lombardy. On Hadamard Series and Rotating Q-Automata. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{dando_et_al:LIPIcs.MFCS.2018.6,
author = {Dando, Louis-Marie and Lombardy, Sylvain},
title = {{On Hadamard Series and Rotating Q-Automata}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {6:1--6:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.6},
URN = {urn:nbn:de:0030-drops-95881},
doi = {10.4230/LIPIcs.MFCS.2018.6},
annote = {Keywords: Rational series, Hadamard operations, Rotating automata, Two-way automata}
}
Document
One-Sided Error Communication Complexity of Gap Hamming Distance
Abstract
Assume that Alice has a binary string x and Bob a binary string y, both strings are of length n. Their goal is to output 0, if x and y are at least L-close in Hamming distance, and output 1, if x and y are at least U-far in Hamming distance, where L < U are some integer parameters known to both parties. If the Hamming distance between x and y lies in the interval (L, U), they are allowed to output anything. This problem is called the Gap Hamming Distance. In this paper we study public-coin one-sided error communication complexity of this problem. The error with probability at most 1/2 is allowed only for pairs at Hamming distance at least U. In this paper we determine this complexity up to factors logarithmic in L. The protocol we construct for the upper bound is simultaneous.
Cite as
Egor Klenin and Alexander Kozachinskiy. One-Sided Error Communication Complexity of Gap Hamming Distance. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{klenin_et_al:LIPIcs.MFCS.2018.7,
author = {Klenin, Egor and Kozachinskiy, Alexander},
title = {{One-Sided Error Communication Complexity of Gap Hamming Distance}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {7:1--7:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.7},
URN = {urn:nbn:de:0030-drops-95893},
doi = {10.4230/LIPIcs.MFCS.2018.7},
annote = {Keywords: Communication Complexity, Gap Hamming Distance, one-sided error}
}
Document
Online Maximum Matching with Recourse
Abstract
We study the online maximum matching problem in a model in which the edges are associated with a known recourse parameter k. An online algorithm for this problem has to maintain a valid matching while edges of the underlying graph are presented one after the other. At any moment the algorithm can decide to include an edge into the matching or to exclude it, under the restriction that at most k such actions per edge take place, where k is typically a small constant. This problem was introduced and studied in the context of general online packing problems with recourse by Avitabile et al. [Avitabile et al., 2013], whereas the special case k=2 was studied by Boyar et al. [Boyar et al., 2017].
In the first part of this paper, we consider the edge arrival model, in which an arriving edge never disappears from the graph. Here, we first show an improved analysis on the performance of the algorithm AMP given in [Avitabile et al., 2013], by exploiting the structure of the matching problem. In addition, we extend the result of [Boyar et al., 2017] and show that the greedy algorithm has competitive ratio 3/2 for every even k and ratio 2 for every odd k. Moreover, we present and analyze an improvement of the greedy algorithm which we call L-Greedy, and we show that for small values of k it outperforms the algorithm of [Avitabile et al., 2013]. In terms of lower bounds, we show that no deterministic algorithm better than 1+1/(k-1) exists, improving upon the lower bound of 1+1/k shown in [Avitabile et al., 2013].
The second part of the paper is devoted to the edge arrival/departure model, which is the fully dynamic variant of online matching with recourse. The analysis of L-Greedy and AMP carry through in this model; moreover we show a lower bound of (k^2-3k+6)/(k^2-4k+7) for all even k >= 4. For k in {2,3}, the competitive ratio is 3/2.
Cite as
Spyros Angelopoulos, Christoph Dürr, and Shendan Jin. Online Maximum Matching with Recourse. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{angelopoulos_et_al:LIPIcs.MFCS.2018.8,
author = {Angelopoulos, Spyros and D\"{u}rr, Christoph and Jin, Shendan},
title = {{Online Maximum Matching with Recourse}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {8:1--8:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.8},
URN = {urn:nbn:de:0030-drops-95908},
doi = {10.4230/LIPIcs.MFCS.2018.8},
annote = {Keywords: Competitive ratio, maximum cardinality matching, recourse}
}
Document
Linking Focusing and Resolution with Selection
Abstract
Focusing and selection are techniques that shrink the proof search space for respectively sequent calculi and resolution. To bring out a link between them, we generalize them both: we introduce a sequent calculus where each occurrence of an atom can have a positive or a negative polarity; and a resolution method where each literal, whatever its sign, can be selected in input clauses. We prove the equivalence between cut-free proofs in this sequent calculus and derivations of the empty clause in that resolution method. Such a generalization is not semi-complete in general, which allows us to consider complete instances that correspond to theories of any logical strength. We present three complete instances: first, our framework allows us to show that ordinary focusing corresponds to hyperresolution and semantic resolution; the second instance is deduction modulo theory; and a new setting, not captured by any existing framework, extends deduction modulo theory with rewriting rules having several left-hand sides, which restricts even more the proof search space.
Cite as
Guillaume Burel. Linking Focusing and Resolution with Selection. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{burel:LIPIcs.MFCS.2018.9,
author = {Burel, Guillaume},
title = {{Linking Focusing and Resolution with Selection}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {9:1--9:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.9},
URN = {urn:nbn:de:0030-drops-95917},
doi = {10.4230/LIPIcs.MFCS.2018.9},
annote = {Keywords: logic in computer science, automated deduction, proof theory, sequent calculus, refinements of resolution, deduction modulo theory, polarization}
}
Document
Team Semantics for the Specification and Verification of Hyperproperties
Abstract
We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a synchronous variant of team semantics. We study basic properties of this new logic and classify the computational complexity of its satisfiability, path, and model checking problem. Further, we examine how extensions of these basic logics react on adding other atomic operators. Finally, we compare its expressivity to the one of HyperLTL, another recently introduced logic for hyperproperties. Our results show that LTL under team semantics is a viable alternative to HyperLTL, which complements the expressivity of HyperLTL and has partially better algorithmic properties.
Cite as
Andreas Krebs, Arne Meier, Jonni Virtema, and Martin Zimmermann. Team Semantics for the Specification and Verification of Hyperproperties. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{krebs_et_al:LIPIcs.MFCS.2018.10,
author = {Krebs, Andreas and Meier, Arne and Virtema, Jonni and Zimmermann, Martin},
title = {{Team Semantics for the Specification and Verification of Hyperproperties}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {10:1--10:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.10},
URN = {urn:nbn:de:0030-drops-95926},
doi = {10.4230/LIPIcs.MFCS.2018.10},
annote = {Keywords: LTL, Hyperproperties, Team Semantics, Model Checking, Satisfiability}
}
Document
Consistency for Counting Quantifiers
Abstract
We apply the algebraic approach for Constraint Satisfaction Problems (CSPs) with counting quantifiers, developed by Bulatov and Hedayaty, for the first time to obtain classifications for computational complexity. We develop the consistency approach for expanding polymorphisms to deduce that, if H has an expanding majority polymorphism, then the corresponding CSP with counting quantifiers is tractable. We elaborate some applications of our result, in particular deriving a complexity classification for partially reflexive graphs endowed with all unary relations. For each such structure, either the corresponding CSP with counting quantifiers is in P, or it is NP-hard.
Cite as
Florent R. Madelaine and Barnaby Martin. Consistency for Counting Quantifiers. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{madelaine_et_al:LIPIcs.MFCS.2018.11,
author = {Madelaine, Florent R. and Martin, Barnaby},
title = {{Consistency for Counting Quantifiers}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {11:1--11:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.11},
URN = {urn:nbn:de:0030-drops-95931},
doi = {10.4230/LIPIcs.MFCS.2018.11},
annote = {Keywords: Quantified Constraints, Constraint Satisfaction, Logic in Computer Science, Universal Algebra, Computational Complexity}
}
Document
The b-Branching Problem in Digraphs
Abstract
In this paper, we introduce the concept of b-branchings in digraphs, which is a generalization of branchings serving as a counterpart of b-matchings. Here b is a positive integer vector on the vertex set of a digraph, and a b-branching is defined as a common independent set of two matroids defined by b: an arc set is a b-branching if it has at most b(v) arcs sharing the terminal vertex v, and it is an independent set of a certain sparsity matroid defined by b. We demonstrate that b-branchings yield an appropriate generalization of branchings by extending several classical results on branchings. We first present a multi-phase greedy algorithm for finding a maximum-weight b-branching. We then prove a packing theorem extending Edmonds' disjoint branchings theorem, and provide a strongly polynomial algorithm for finding optimal disjoint b-branchings. As a consequence of the packing theorem, we prove the integer decomposition property of the b-branching polytope. Finally, we deal with a further generalization in which a matroid constraint is imposed on the b(v) arcs sharing the terminal vertex v.
Cite as
Naonori Kakimura, Naoyuki Kamiyama, and Kenjiro Takazawa. The b-Branching Problem in Digraphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{kakimura_et_al:LIPIcs.MFCS.2018.12,
author = {Kakimura, Naonori and Kamiyama, Naoyuki and Takazawa, Kenjiro},
title = {{The b-Branching Problem in Digraphs}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {12:1--12:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.12},
URN = {urn:nbn:de:0030-drops-95948},
doi = {10.4230/LIPIcs.MFCS.2018.12},
annote = {Keywords: Greedy Algorithm, Packing, Matroid Intersection, Sparsity Matroid, Arborescence}
}
Document
Pairing heaps: the forward variant
Abstract
The pairing heap is a classical heap data structure introduced in 1986 by Fredman, Sedgewick, Sleator, and Tarjan. It is remarkable both for its simplicity and for its excellent performance in practice. The "magic" of pairing heaps lies in the restructuring that happens after the deletion of the smallest item. The resulting collection of trees is consolidated in two rounds: a left-to-right pairing round, followed by a right-to-left accumulation round. Fredman et al. showed, via an elegant correspondence to splay trees, that in a pairing heap of size n all heap operations take O(log n) amortized time. They also proposed an arguably more natural variant, where both pairing and accumulation are performed in a combined left-to-right round (called the forward variant of pairing heaps). The analogy to splaying breaks down in this case, and the analysis of the forward variant was left open.
In this paper we show that inserting an item and deleting the minimum in a forward-variant pairing heap both take amortized time O(log(n) * 4^(sqrt(log n))). This is the first improvement over the O(sqrt(n)) bound showed by Fredman et al. three decades ago. Our analysis relies on a new potential function that tracks parent-child rank-differences in the heap.
Cite as
Dani Dorfman, Haim Kaplan, László Kozma, and Uri Zwick. Pairing heaps: the forward variant. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{dorfman_et_al:LIPIcs.MFCS.2018.13,
author = {Dorfman, Dani and Kaplan, Haim and Kozma, L\'{a}szl\'{o} and Zwick, Uri},
title = {{Pairing heaps: the forward variant}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {13:1--13:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.13},
URN = {urn:nbn:de:0030-drops-95956},
doi = {10.4230/LIPIcs.MFCS.2018.13},
annote = {Keywords: data structure, priority queue, pairing heap}
}
Document
Simultaneous Multiparty Communication Protocols for Composed Functions
Abstract
The Number On the Forehead (NOF) model is a multiparty communication game between k players that collaboratively want to evaluate a given function F : X_1 x *s x X_k - > Y on some input (x_1,...,x_k) by broadcasting bits according to a predetermined protocol. The input is distributed in such a way that each player i sees all of it except x_i (as if x_i is written on the forehead of player i). In the Simultaneous Message Passing (SMP) model, the players have the extra condition that they cannot speak to each other, but instead send information to a referee. The referee does not know the players' inputs, and cannot give any information back. At the end, the referee must be able to recover F(x_1,...,x_k) from what she obtained from the players.
A central open question in the simultaneous NOF model, called the log n barrier, is to find a function which is hard to compute when the number of players is polylog(n) or more (where the x_i's have size poly(n)). This has an important application in circuit complexity, as it could help to separate ACC^0 from other complexity classes [Håstad and Goldmann, 1991; Babai et al., 2004]. One of the candidates for breaking the log n barrier belongs to the family of composed functions. The input to these functions in the k-party NOF model is represented by a k x (t * n) boolean matrix M, whose row i is the number x_i on the forehead of player i and t is a block-width parameter. A symmetric composed function acting on M is specified by two symmetric n- and kt-variate functions f and g (respectively), that output f o g(M) = f(g(B_1),...,g(B_n)) where B_j is the j-th block of width t of M. As the majority function Maj is conjectured to be outside of ACC^0, Babai et. al. [Babai et al., 1995; Babai et al., 2004] suggested to study the composed function Maj o Maj_t, with t large enough, for breaking the log n barrier (where Maj_t outputs 1 if at least kt/2 bits of the input block are set to 1).
So far, it was only known that block-width t = 1 is not enough for Maj o Maj_t to break the log n barrier in the simultaneous NOF model [Babai et al., 2004] (Chattopadhyay and Saks [Chattopadhyay and Saks, 2014] found an efficient protocol for t <= polyloglog(n), but it requires randomness to be simultaneous). In this paper, we extend this result to any constant block-width t > 1 by giving a deterministic simultaneous protocol of cost 2^O(2^t) log^(2^(t+1))(n) for any symmetric composed function f o g (which includes Maj o Maj_t) when there are more than 2^Omega(2^t) log n players.
Cite as
Yassine Hamoudi. Simultaneous Multiparty Communication Protocols for Composed Functions. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{hamoudi:LIPIcs.MFCS.2018.14,
author = {Hamoudi, Yassine},
title = {{Simultaneous Multiparty Communication Protocols for Composed Functions}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {14:1--14:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.14},
URN = {urn:nbn:de:0030-drops-95969},
doi = {10.4230/LIPIcs.MFCS.2018.14},
annote = {Keywords: Communication complexity, Number On the Forehead model, Simultaneous Message Passing, Log n barrier, Symmetric Composed functions}
}
Document
Sliding Windows over Context-Free Languages
Abstract
We study the space complexity of sliding window streaming algorithms that check membership of the window content in a fixed context-free language. For regular languages, this complexity is either constant, logarithmic or linear [Moses Ganardi et al., 2016]. We prove that every context-free language whose sliding window space complexity is log_2(n) - omega(1) must be regular and has constant space complexity. Moreover, for every c in N, c >= 1 we construct a (nondeterministic) context-free language whose sliding window space complexity is O(n^(1/c)) \ o(n^(1/c)). Finally, we give an example of a deterministic one-counter language whose sliding window space complexity is Theta((log n)^2).
Cite as
Moses Ganardi, Artur Jez, and Markus Lohrey. Sliding Windows over Context-Free Languages. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{ganardi_et_al:LIPIcs.MFCS.2018.15,
author = {Ganardi, Moses and Jez, Artur and Lohrey, Markus},
title = {{Sliding Windows over Context-Free Languages}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {15:1--15:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.15},
URN = {urn:nbn:de:0030-drops-95973},
doi = {10.4230/LIPIcs.MFCS.2018.15},
annote = {Keywords: sliding windows, streaming algorithms, context-free languages}
}
Document
Average Case Analysis of Leaf-Centric Binary Tree Sources
Abstract
We study the average size of the minimal directed acyclic graph (DAG) with respect to so-called leaf-centric binary tree sources as studied by Zhang, Yang, and Kieffer. A leaf-centric binary tree source induces for every n >= 2 a probability distribution on all binary trees with n leaves. We generalize a result shown by Flajolet, Gourdon, Martinez and Devroye according to which the average size of the minimal DAG of a binary tree that is produced by the binary search tree model is Theta(n / log n).
Cite as
Louisa Seelbach Benkner and Markus Lohrey. Average Case Analysis of Leaf-Centric Binary Tree Sources. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{seelbachbenkner_et_al:LIPIcs.MFCS.2018.16,
author = {Seelbach Benkner, Louisa and Lohrey, Markus},
title = {{Average Case Analysis of Leaf-Centric Binary Tree Sources}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {16:1--16:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.16},
URN = {urn:nbn:de:0030-drops-95982},
doi = {10.4230/LIPIcs.MFCS.2018.16},
annote = {Keywords: Directed acylic graphs, average case analysis, tree compression}
}
Document
Expressive Power, Satisfiability and Equivalence of Circuits over Nilpotent Algebras
Abstract
Satisfiability of Boolean circuits is NP-complete in general but becomes polynomial time when restricted for example either to monotone gates or linear gates. We go outside Boolean realm and consider circuits built of any fixed set of gates on an arbitrary large finite domain. From the complexity point of view this is connected with solving equations over finite algebras. This in turn is one of the oldest and well-known mathematical problems which for centuries was the driving force of research in algebra. Let us only mention Galois theory, Gaussian elimination or Diophantine Equations. The last problem has been shown to be undecidable, however in finite realms such problems are obviously decidable in nondeterministic polynomial time.
A project of characterizing finite algebras m A with polynomial time algorithms deciding satisfiability of circuits over m A has been undertaken in [Pawel M. Idziak and Jacek Krzaczkowski, 2018]. Unfortunately that paper leaves a gap for nilpotent but not supernilpotent algebras. In this paper we discuss possible attacks on filling this gap.
Cite as
Pawel M. Idziak, Piotr Kawalek, and Jacek Krzaczkowski. Expressive Power, Satisfiability and Equivalence of Circuits over Nilpotent Algebras. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{idziak_et_al:LIPIcs.MFCS.2018.17,
author = {Idziak, Pawel M. and Kawalek, Piotr and Krzaczkowski, Jacek},
title = {{Expressive Power, Satisfiability and Equivalence of Circuits over Nilpotent Algebras}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {17:1--17:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.17},
URN = {urn:nbn:de:0030-drops-95993},
doi = {10.4230/LIPIcs.MFCS.2018.17},
annote = {Keywords: circuit satisfiability, solving equations, Constraint Satisfaction Problem, structure theory}
}
Document
Lagrange's Theorem for Binary Squares
Abstract
We show how to prove theorems in additive number theory using a decision procedure based on finite automata. Among other things, we obtain the following analogue of Lagrange's theorem: every natural number > 686 is the sum of at most 4 natural numbers whose canonical base-2 representation is a binary square, that is, a string of the form xx for some block of bits x. Here the number 4 is optimal. While we cannot embed this theorem itself in a decidable theory, we show that stronger lemmas that imply the theorem can be embedded in decidable theories, and show how automated methods can be used to search for these stronger lemmas.
Cite as
P. Madhusudan, Dirk Nowotka, Aayush Rajasekaran, and Jeffrey Shallit. Lagrange's Theorem for Binary Squares. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{madhusudan_et_al:LIPIcs.MFCS.2018.18,
author = {Madhusudan, P. and Nowotka, Dirk and Rajasekaran, Aayush and Shallit, Jeffrey},
title = {{Lagrange's Theorem for Binary Squares}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {18:1--18:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.18},
URN = {urn:nbn:de:0030-drops-96003},
doi = {10.4230/LIPIcs.MFCS.2018.18},
annote = {Keywords: binary square, theorem-proving, finite automaton, decision procedure, decidable theory, additive number theory}
}
Document
A Two-Sided Error Distributed Property Tester For Conductance
Abstract
We study property testing in the distributed model and extend its setting from testing with one-sided error to testing with two-sided error. In particular, we develop a two-sided error property tester for general graphs with round complexity O(log(n) / (epsilon Phi^2)) in the CONGEST model, which accepts graphs with conductance Phi and rejects graphs that are epsilon-far from having conductance at least Phi^2 / 1000 with constant probability. Our main insight is that one can start poly(n) random walks from a few random vertices without violating the congestion and unite the results to obtain a consistent answer from all vertices. For connected graphs, this is even possible when the number of vertices is unknown. We also obtain a matching Omega(log n) lower bound for the LOCAL and CONGEST models by an indistinguishability argument. Although the power of vertex labels that arises from two-sided error might seem to be much stronger than in the sequential query model, we can show that this is not the case.
Cite as
Hendrik Fichtenberger and Yadu Vasudev. A Two-Sided Error Distributed Property Tester For Conductance. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{fichtenberger_et_al:LIPIcs.MFCS.2018.19,
author = {Fichtenberger, Hendrik and Vasudev, Yadu},
title = {{A Two-Sided Error Distributed Property Tester For Conductance}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {19:1--19:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.19},
URN = {urn:nbn:de:0030-drops-96019},
doi = {10.4230/LIPIcs.MFCS.2018.19},
annote = {Keywords: property testing, distributed algorithms, conductance}
}
Document
Graph Similarity and Approximate Isomorphism
Abstract
The graph similarity problem, also known as approximate graph isomorphism or graph matching problem, has been extensively studied in the machine learning community, but has not received much attention in the algorithms community: Given two graphs G,H of the same order n with adjacency matrices A_G,A_H, a well-studied measure of similarity is the Frobenius distance dist(G,H):=min_{pi}|A_G^{pi}-A_H|_F, where pi ranges over all permutations of the vertex set of G, where A_G^pi denotes the matrix obtained from A_G by permuting rows and columns according to pi, and where |M |_F is the Frobenius norm of a matrix M. The (weighted) graph similarity problem, denoted by GSim (WSim), is the problem of computing this distance for two graphs of same order. This problem is closely related to the notoriously hard quadratic assignment problem (QAP), which is known to be NP-hard even for severely restricted cases.
It is known that GSim (WSim) is NP-hard; we strengthen this hardness result by showing that the problem remains NP-hard even for the class of trees. Identifying the boundary of tractability for WSim is best done in the framework of linear algebra. We show that WSim is NP-hard as long as one of the matrices has unbounded rank or negative eigenvalues: hence, the realm of tractability is restricted to positive semi-definite matrices of bounded rank. Our main result is a polynomial time algorithm for the special case where the associated (weighted) adjacency graph for one of the matrices has a bounded number of twin equivalence classes. The key parameter underlying our algorithm is the clustering number of a graph; this parameter arises in context of the spectral graph drawing machinery.
Cite as
Martin Grohe, Gaurav Rattan, and Gerhard J. Woeginger. Graph Similarity and Approximate Isomorphism. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{grohe_et_al:LIPIcs.MFCS.2018.20,
author = {Grohe, Martin and Rattan, Gaurav and Woeginger, Gerhard J.},
title = {{Graph Similarity and Approximate Isomorphism}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {20:1--20:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.20},
URN = {urn:nbn:de:0030-drops-96021},
doi = {10.4230/LIPIcs.MFCS.2018.20},
annote = {Keywords: Graph Similarity, Quadratic Assignment Problem, Approximate Graph Isomorphism}
}
Document
Finding Short Synchronizing Words for Prefix Codes
Abstract
We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is defined by its literal decoder (whose size is polynomially equivalent to the total length of all words in the code). For the first case for every epsilon > 0 we prove n^(1 - epsilon)-inapproximability for recognizable binary maximal prefix codes, Theta(log n)-inapproximability for finite binary maximal prefix codes and n^(1/2 - epsilon)-inapproximability for finite binary prefix codes. By c-inapproximability here we mean the non-existence of a c-approximation polynomial time algorithm under the assumption P != NP, and by n the number of states of the decoder in the input. For the second case, we propose approximation and exact algorithms and conjecture that for finite maximal prefix codes the problem can be solved in polynomial time. We also study the related problems of finding a shortest mortal and a shortest avoiding word.
Cite as
Andrew Ryzhikov and Marek Szykula. Finding Short Synchronizing Words for Prefix Codes. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{ryzhikov_et_al:LIPIcs.MFCS.2018.21,
author = {Ryzhikov, Andrew and Szykula, Marek},
title = {{Finding Short Synchronizing Words for Prefix Codes}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {21:1--21:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.21},
URN = {urn:nbn:de:0030-drops-96037},
doi = {10.4230/LIPIcs.MFCS.2018.21},
annote = {Keywords: synchronizing word, mortal word, avoiding word, Huffman decoder, inapproximability}
}
Document
Quantum vs. Classical Proofs and Subset Verification
Abstract
We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only classical witnesses, cannot verify certain properties of subsets given implicitly via an oracle. We use this framework to prove an oracle separation between QCMA and QMA using an "in-place" permutation oracle, making the first progress on this question since Aaronson and Kuperberg in 2007 [Aaronson and Kuperberg, 2007]. We also use the framework to prove a particularly simple standard oracle separation between QCMA and AM.
Cite as
Bill Fefferman and Shelby Kimmel. Quantum vs. Classical Proofs and Subset Verification. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 22:1-22:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{fefferman_et_al:LIPIcs.MFCS.2018.22,
author = {Fefferman, Bill and Kimmel, Shelby},
title = {{Quantum vs. Classical Proofs and Subset Verification}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {22:1--22:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.22},
URN = {urn:nbn:de:0030-drops-96040},
doi = {10.4230/LIPIcs.MFCS.2018.22},
annote = {Keywords: Quantum Complexity Theory, Quantum Proofs}
}
Document
Timed Network Games with Clocks
Abstract
Network games are widely used as a model for selfish resource-allocation problems. In the classical model, each player selects a path connecting her source and target vertices. The cost of traversing an edge depends on the load; namely, number of players that traverse it. Thus, it abstracts the fact that different users may use a resource at different times and for different durations, which plays an important role in determining the costs of the users in reality. For example, when transmitting packets in a communication network, routing traffic in a road network, or processing a task in a production system, actual sharing and congestion of resources crucially depends on time.
In [G. Avni et al., 2017], we introduced timed network games, which add a time component to network games. Each vertex v in the network is associated with a cost function, mapping the load on v to the price that a player pays for staying in v for one time unit with this load. Each edge in the network is guarded by the time intervals in which it can be traversed, which forces the players to spend time in the vertices. In this work we significantly extend the way time can be referred to in timed network games. In the model we study, the network is equipped with clocks, and, as in timed automata, edges are guarded by constraints on the values of the clocks, and their traversal may involve a reset of some clocks. We argue that the stronger model captures many realistic networks. The addition of clocks breaks the techniques we developed in [G. Avni et al., 2017] and we develop new techniques in order to show that positive results on classic network games carry over to the stronger timed setting.
Cite as
Guy Avni, Shibashis Guha, and Orna Kupferman. Timed Network Games with Clocks. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{avni_et_al:LIPIcs.MFCS.2018.23,
author = {Avni, Guy and Guha, Shibashis and Kupferman, Orna},
title = {{Timed Network Games with Clocks}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {23:1--23:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.23},
URN = {urn:nbn:de:0030-drops-96053},
doi = {10.4230/LIPIcs.MFCS.2018.23},
annote = {Keywords: Network games, Timed automata, Nash equilibrium, Equilibrium inefficiency}
}
Document
Hardness Results for Consensus-Halving
Abstract
The Consensus-halving problem is the problem of dividing an object into two portions, such that each of n agents has equal valuation for the two portions. We study the epsilon-approximate version, which allows each agent to have an epsilon discrepancy on the values of the portions. It was recently proven in [Filos-Ratsikas and Goldberg, 2018] that the problem of computing an epsilon-approximate Consensus-halving solution (for n agents and n cuts) is PPA-complete when epsilon is inverse-exponential. In this paper, we prove that when epsilon is constant, the problem is PPAD-hard and the problem remains PPAD-hard when we allow a constant number of additional cuts. Additionally, we prove that deciding whether a solution with n-1 cuts exists for the problem is NP-hard.
Cite as
Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg, and Jie Zhang. Hardness Results for Consensus-Halving. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{filosratsikas_et_al:LIPIcs.MFCS.2018.24,
author = {Filos-Ratsikas, Aris and Frederiksen, S{\o}ren Kristoffer Stiil and Goldberg, Paul W. and Zhang, Jie},
title = {{Hardness Results for Consensus-Halving}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {24:1--24:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.24},
URN = {urn:nbn:de:0030-drops-96069},
doi = {10.4230/LIPIcs.MFCS.2018.24},
annote = {Keywords: PPAD, PPA, consensus halving, generalized-circuit, reduction}
}
Document
Maximum Rooted Connected Expansion
Abstract
Prefetching constitutes a valuable tool toward the goal of efficient Web surfing. As a result, estimating the amount of resources that need to be preloaded during a surfer's browsing becomes an important task. In this regard, prefetching can be modeled as a two-player combinatorial game [Fomin et al., Theoretical Computer Science 2014], where a surfer and a marker alternately play on a given graph (representing the Web graph). During its turn, the marker chooses a set of k nodes to mark (prefetch), whereas the surfer, represented as a token resting on graph nodes, moves to a neighboring node (Web resource). The surfer's objective is to reach an unmarked node before all nodes become marked and the marker wins. Intuitively, since the surfer is step-by-step traversing a subset of nodes in the Web graph, a satisfactory prefetching procedure would load in cache (without any delay) all resources lying in the neighborhood of this growing subset.
Motivated by the above, we consider the following maximization problem to which we refer to as the Maximum Rooted Connected Expansion (MRCE) problem. Given a graph G and a root node v_0, we wish to find a subset of vertices S such that S is connected, S contains v_0 and the ratio |N[S]|/|S| is maximized, where N[S] denotes the closed neighborhood of S, that is, N[S] contains all nodes in S and all nodes with at least one neighbor in S.
We prove that the problem is NP-hard even when the input graph G is restricted to be a split graph. On the positive side, we demonstrate a polynomial time approximation scheme for split graphs. Furthermore, we present a 1/6(1-1/e)-approximation algorithm for general graphs based on techniques for the Budgeted Connected Domination problem [Khuller et al., SODA 2014]. Finally, we provide a polynomial-time algorithm for the special case of interval graphs. Our algorithm returns an optimal solution for MRCE in O(n^3) time, where n is the number of nodes in G.
Cite as
Ioannis Lamprou, Russell Martin, Sven Schewe, Ioannis Sigalas, and Vassilis Zissimopoulos. Maximum Rooted Connected Expansion. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{lamprou_et_al:LIPIcs.MFCS.2018.25,
author = {Lamprou, Ioannis and Martin, Russell and Schewe, Sven and Sigalas, Ioannis and Zissimopoulos, Vassilis},
title = {{Maximum Rooted Connected Expansion}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {25:1--25:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.25},
URN = {urn:nbn:de:0030-drops-96076},
doi = {10.4230/LIPIcs.MFCS.2018.25},
annote = {Keywords: prefetching, domination, expansion, ratio}
}
Document
Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups
Abstract
In this paper we consider what can be computed by a user interacting with a potentially malicious server, when the server performs polynomial-time quantum computation but the user can only perform polynomial-time classical (i.e., non-quantum) computation. Understanding the computational power of this model, which corresponds to polynomial-time quantum computation that can be efficiently verified classically, is a well-known open problem in quantum computing. Our result shows that computing the order of a solvable group, which is one of the most general problems for which quantum computing exhibits an exponential speed-up with respect to classical computing, can be realized in this model.
Cite as
François Le Gall, Tomoyuki Morimae, Harumichi Nishimura, and Yuki Takeuchi. Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{legall_et_al:LIPIcs.MFCS.2018.26,
author = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki and Nishimura, Harumichi and Takeuchi, Yuki},
title = {{Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {26:1--26:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.26},
URN = {urn:nbn:de:0030-drops-96087},
doi = {10.4230/LIPIcs.MFCS.2018.26},
annote = {Keywords: Quantum computing, interactive proofs, group-theoretic problems}
}
Document
On the Complexity of Team Logic and Its Two-Variable Fragment
Abstract
We study the logic FO(~), the extension of first-order logic with team semantics by unrestricted Boolean negation. It was recently shown to be axiomatizable, but otherwise has not yet received much attention in questions of computational complexity. In this paper, we consider its two-variable fragment FO^2(~) and prove that its satisfiability problem is decidable, and in fact complete for the recently introduced non-elementary class TOWER(poly). Moreover, we classify the complexity of model checking of FO(~) with respect to the number of variables and the quantifier rank, and prove a dichotomy between PSPACE- and ATIME-ALT(exp, poly)-complete fragments. For the lower bounds, we propose a translation from modal team logic MTL to FO^2(~) that extends the well-known standard translation from modal logic ML to FO^2. For the upper bounds, we translate FO(~) to fragments of second-order logic with PSPACE-complete and ATIME-ALT(exp, poly)-complete model checking, respectively.
Cite as
Martin Lück. On the Complexity of Team Logic and Its Two-Variable Fragment. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 27:1-27:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{luck:LIPIcs.MFCS.2018.27,
author = {L\"{u}ck, Martin},
title = {{On the Complexity of Team Logic and Its Two-Variable Fragment}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {27:1--27:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.27},
URN = {urn:nbn:de:0030-drops-96094},
doi = {10.4230/LIPIcs.MFCS.2018.27},
annote = {Keywords: team logic, two-variable logic, complexity, satisfiability, model checking}
}
Document
A Tight Analysis of the Parallel Undecided-State Dynamics with Two Colors
Abstract
The Undecided-State Dynamics is a well-known protocol for distributed consensus. We analyze it in the parallel PULL communication model on the complete graph with n nodes for the binary case (every node can either support one of two possible colors, or be in the undecided state).
An interesting open question is whether this dynamics is an efficient Self-Stabilizing protocol, namely, starting from an arbitrary initial configuration, it reaches consensus quickly (i.e., within a polylogarithmic number of rounds). Previous work in this setting only considers initial color configurations with no undecided nodes and a large bias (i.e., Theta(n)) towards the majority color.
In this paper we present an unconditional analysis of the Undecided-State Dynamics that answers to the above question in the affirmative. We prove that, starting from any initial configuration, the process reaches a monochromatic configuration within O(log n) rounds, with high probability. This bound turns out to be tight. Our analysis also shows that, if the initial configuration has bias Omega(sqrt(n log n)), then the dynamics converges toward the initial majority color, with high probability.
Cite as
Andrea Clementi, Mohsen Ghaffari, Luciano Gualà, Emanuele Natale, Francesco Pasquale, and Giacomo Scornavacca. A Tight Analysis of the Parallel Undecided-State Dynamics with Two Colors. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{clementi_et_al:LIPIcs.MFCS.2018.28,
author = {Clementi, Andrea and Ghaffari, Mohsen and Gual\`{a}, Luciano and Natale, Emanuele and Pasquale, Francesco and Scornavacca, Giacomo},
title = {{A Tight Analysis of the Parallel Undecided-State Dynamics with Two Colors}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {28:1--28:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.28},
URN = {urn:nbn:de:0030-drops-96107},
doi = {10.4230/LIPIcs.MFCS.2018.28},
annote = {Keywords: Distributed Consensus, Self-Stabilization, PULL Model, Markov Chains}
}
Document
Recovering Sparse Graphs
Abstract
We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G' obtained from a d-degenerate graph G by complementing on at most k arbitrary subsets of the vertex set of G and outputs a graph H such that G and H agree on all but f(d,k) vertices.
Our work is motivated by the first order model checking in graph classes that are first order interpretable in classes of sparse graphs. We derive as a corollary that if G is a graph class with bounded expansion, then the first order model checking is fixed parameter tractable in the class of all graphs that can obtained from a graph G in G by complementing on at most k arbitrary subsets of the vertex set of G; this implies an earlier result that the first order model checking is fixed parameter tractable in graph classes interpretable in classes of graphs with bounded maximum degree.
Cite as
Jakub Gajarský and Daniel Král'. Recovering Sparse Graphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{gajarsky_et_al:LIPIcs.MFCS.2018.29,
author = {Gajarsk\'{y}, Jakub and Kr\'{a}l', Daniel},
title = {{Recovering Sparse Graphs}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {29:1--29:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.29},
URN = {urn:nbn:de:0030-drops-96111},
doi = {10.4230/LIPIcs.MFCS.2018.29},
annote = {Keywords: model checking, degenerate graphs, interpretations, bounded expansion}
}
Document
Average-Case Polynomial-Time Computability of Hamiltonian Dynamics
Abstract
We apply average-case complexity theory to physical problems modeled by continuous-time dynamical systems. The computational complexity when simulating such systems for a bounded time-frame mainly stems from trajectories coming close to complex singularities of the system. We show that if for most initial values the trajectories do not come close to singularities the simulation can be done in polynomial time on average. For Hamiltonian systems we relate this to the volume of "almost singularities" in phase space and give some general criteria to show that a Hamiltonian system can be simulated efficiently on average. As an application we show that the planar circular-restricted three-body problem is average-case polynomial-time computable.
Cite as
Akitoshi Kawamura, Holger Thies, and Martin Ziegler. Average-Case Polynomial-Time Computability of Hamiltonian Dynamics. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{kawamura_et_al:LIPIcs.MFCS.2018.30,
author = {Kawamura, Akitoshi and Thies, Holger and Ziegler, Martin},
title = {{Average-Case Polynomial-Time Computability of Hamiltonian Dynamics}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {30:1--30:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.30},
URN = {urn:nbn:de:0030-drops-96125},
doi = {10.4230/LIPIcs.MFCS.2018.30},
annote = {Keywords: Computable Analysis, Real computation, Dynamical systems, Average-case complexity, Computation in physics}
}
Document
Generalized Budgeted Submodular Set Function Maximization
Abstract
In this paper we consider a generalization of the well-known budgeted maximum coverage problem. We are given a ground set of elements and a set of bins. The goal is to find a subset of elements along with an associated set of bins, such that the overall cost is at most a given budget, and the profit is maximized. Each bin has its own cost and the cost of each element depends on its associated bin. The profit is measured by a monotone submodular function over the elements.
We first present an algorithm that guarantees an approximation factor of 1/2(1-1/e^alpha), where alpha <= 1 is the approximation factor of an algorithm for a sub-problem. We give two polynomial-time algorithms to solve this sub-problem. The first one gives us alpha=1- epsilon if the costs satisfies a specific condition, which is fulfilled in several relevant cases, including the unitary costs case and the problem of maximizing a monotone submodular function under a knapsack constraint. The second one guarantees alpha=1-1/e-epsilon for the general case. The gap between our approximation guarantees and the known inapproximability bounds is 1/2.
We extend our algorithm to a bi-criterion approximation algorithm in which we are allowed to spend an extra budget up to a factor beta >= 1 to guarantee a 1/2(1-1/e^(alpha beta))-approximation. If we set beta=1/(alpha)ln (1/(2 epsilon)), the algorithm achieves an approximation factor of 1/2-epsilon, for any arbitrarily small epsilon>0.
Cite as
Francesco Cellinese, Gianlorenzo D'Angelo, Gianpiero Monaco, and Yllka Velaj. Generalized Budgeted Submodular Set Function Maximization. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{cellinese_et_al:LIPIcs.MFCS.2018.31,
author = {Cellinese, Francesco and D'Angelo, Gianlorenzo and Monaco, Gianpiero and Velaj, Yllka},
title = {{Generalized Budgeted Submodular Set Function Maximization}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {31:1--31:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.31},
URN = {urn:nbn:de:0030-drops-96138},
doi = {10.4230/LIPIcs.MFCS.2018.31},
annote = {Keywords: Submodular set function, Approximation algorithms, Budgeted Maximum Coverage}
}
Document
Complexity of Preimage Problems for Deterministic Finite Automata
Abstract
Given a subset of states S of a deterministic finite automaton and a word w, the preimage is the subset of all states that are mapped to a state from S by the action of w. We study the computational complexity of three problems related to the existence of words yielding certain preimages, which are especially motivated by the theory of synchronizing automata. The first problem is whether, for a given subset, there exists a word extending the subset (giving a larger preimage). The second problem is whether there exists a word totally extending the subset (giving the whole set of states) - it is equivalent to the problem whether there exists an avoiding word for the complementary subset. The third problem is whether there exists a word resizing the subset (giving a preimage of a different size). We also consider the variants of the problem where an upper bound on the length of the word is given in the input. Because in most cases our problems are computationally hard, we additionally consider parametrized complexity by the size of the given subset. We focus on the most interesting cases that are the subclasses of strongly connected, synchronizing, and binary automata.
Cite as
Mikhail V. Berlinkov, Robert Ferens, and Marek Szykula. Complexity of Preimage Problems for Deterministic Finite Automata. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{berlinkov_et_al:LIPIcs.MFCS.2018.32,
author = {Berlinkov, Mikhail V. and Ferens, Robert and Szykula, Marek},
title = {{Complexity of Preimage Problems for Deterministic Finite Automata}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {32:1--32:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.32},
URN = {urn:nbn:de:0030-drops-96149},
doi = {10.4230/LIPIcs.MFCS.2018.32},
annote = {Keywords: avoiding word, extending word, extensible subset, reset word, synchronizing automaton}
}
Document
The Complexity of Disjunctive Linear Diophantine Constraints
Abstract
We study the Constraint Satisfaction Problem CSP( A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.
Cite as
Manuel Bodirsky, Barnaby Martin, Marcello Mamino, and Antoine Mottet. The Complexity of Disjunctive Linear Diophantine Constraints. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{bodirsky_et_al:LIPIcs.MFCS.2018.33,
author = {Bodirsky, Manuel and Martin, Barnaby and Mamino, Marcello and Mottet, Antoine},
title = {{The Complexity of Disjunctive Linear Diophantine Constraints}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {33:1--33:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.33},
URN = {urn:nbn:de:0030-drops-96150},
doi = {10.4230/LIPIcs.MFCS.2018.33},
annote = {Keywords: Constraint Satisfaction, Presburger Arithmetic, Computational Complexity}
}
Document
Give Me Some Slack: Efficient Network Measurements
Abstract
Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast memory in routers. In this work, we study the impact of allowing slack in the window size on the asymptotic requirements of sliding window problems. That is, the algorithm can dynamically adjust the window size between W and W(1+tau) where tau is a small positive parameter. We demonstrate this model's attractiveness by showing that it enables efficient algorithms to problems such as Maximum and General-Summing that require Omega(W) bits even for constant factor approximations in the exact sliding window model. Additionally, for problems that admit sub-linear approximation algorithms such as Basic-Summing and Count-Distinct, the slack model enables a further asymptotic improvement.
The main focus of the paper is on the widely studied Basic-Summing problem of computing the sum of the last W integers from {0,1 ...,R} in a stream. While it is known that Omega(W log R) bits are needed in the exact window model, we show that approximate windows allow an exponential space reduction for constant tau.
Specifically, for tau=Theta(1), we present a space lower bound of Omega(log(RW)) bits. Additionally, we show an Omega(log (W/epsilon)) lower bound for RW epsilon additive approximations and a Omega(log (W/epsilon)+log log R) bits lower bound for (1+epsilon) multiplicative approximations. Our work is the first to study this problem in the exact and additive approximation settings. For all settings, we provide memory optimal algorithms that operate in worst case constant time. This strictly improves on the work of [Mayur Datar et al., 2002] for (1+epsilon)-multiplicative approximation that requires O(epsilon^(-1) log(RW)log log (RW)) space and performs updates in O(log (RW)) worst case time. Finally, we show asymptotic improvements for the Count-Distinct, General-Summing and Maximum problems.
Cite as
Ran Ben Basat, Gil Einziger, and Roy Friedman. Give Me Some Slack: Efficient Network Measurements. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{benbasat_et_al:LIPIcs.MFCS.2018.34,
author = {Ben Basat, Ran and Einziger, Gil and Friedman, Roy},
title = {{Give Me Some Slack: Efficient Network Measurements}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {34:1--34:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.34},
URN = {urn:nbn:de:0030-drops-96165},
doi = {10.4230/LIPIcs.MFCS.2018.34},
annote = {Keywords: Streaming, Network Measurements, Statistics, Lower Bounds}
}
Document
Spanning-Tree Games
Abstract
We introduce and study a game variant of the classical spanning-tree problem. Our spanning-tree game is played between two players, min and max, who alternate turns in jointly constructing a spanning tree of a given connected weighted graph G. Starting with the empty graph, in each turn a player chooses an edge that does not close a cycle in the forest that has been generated so far and adds it to that forest. The game ends when the chosen edges form a spanning tree in G. The goal of min is to minimize the weight of the resulting spanning tree and the goal of max is to maximize it. A strategy for a player is a function that maps each forest in G to an edge that is not yet in the forest and does not close a cycle.
We show that while in the classical setting a greedy approach is optimal, the game setting is more complicated: greedy strategies, namely ones that choose in each turn the lightest (min) or heaviest (max) legal edge, are not necessarily optimal, and calculating their values is NP-hard. We study the approximation ratio of greedy strategies. We show that while a greedy strategy for min guarantees nothing, the performance of a greedy strategy for max is satisfactory: it guarantees that the weight of the generated spanning tree is at least w(MST(G))/2, where w(MST(G)) is the weight of a maximum spanning tree in G, and its approximation ratio with respect to an optimal strategy for max is 1.5+1/w(MST(G)), assuming weights in [0,1]. We also show that these bounds are tight. Moreover, in a stochastic setting, where weights for the complete graph K_n are chosen at random from [0,1], the expected performance of greedy strategies is asymptotically optimal. Finally, we study some variants of the game and study an extension of our results to games on general matroids.
Cite as
Dan Hefetz, Orna Kupferman, Amir Lellouche, and Gal Vardi. Spanning-Tree Games. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{hefetz_et_al:LIPIcs.MFCS.2018.35,
author = {Hefetz, Dan and Kupferman, Orna and Lellouche, Amir and Vardi, Gal},
title = {{Spanning-Tree Games}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {35:1--35:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.35},
URN = {urn:nbn:de:0030-drops-96171},
doi = {10.4230/LIPIcs.MFCS.2018.35},
annote = {Keywords: Algorithms, Games, Minimum/maximum spanning tree, Greedy algorithms}
}
Document
Faster Exploration of Degree-Bounded Temporal Graphs
Abstract
A temporal graph can be viewed as a sequence of static graphs indexed by discrete time steps. The vertex set of each graph in the sequence remains the same; however, the edge sets are allowed to differ. A natural problem on temporal graphs is the Temporal Exploration problem (TEXP): given, as input, a temporal graph G of order n, we are tasked with computing an exploration schedule (i.e., a temporal walk that visits all vertices in G), such that the time step at which the walk arrives at the last unvisited vertex is minimised (we refer to this time step as the arrival time). It can be easily shown that general temporal graphs admit exploration schedules with arrival time no greater than O(n^2). Moreover, it has been shown previously that there exists an infinite family of temporal graphs for which any exploration schedule has arrival time Omega(n^2), making these bounds tight for general TEXP instances. We consider restricted instances of TEXP, in which the temporal graph given as input is, in every time step, of maximum degree d; we show an O(n^2/log n) bound on the arrival time when d is constant, and an O(d log d * n^2/log n) bound when d is given as some function of n.
Cite as
Thomas Erlebach and Jakob T. Spooner. Faster Exploration of Degree-Bounded Temporal Graphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{erlebach_et_al:LIPIcs.MFCS.2018.36,
author = {Erlebach, Thomas and Spooner, Jakob T.},
title = {{Faster Exploration of Degree-Bounded Temporal Graphs}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {36:1--36:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.36},
URN = {urn:nbn:de:0030-drops-96181},
doi = {10.4230/LIPIcs.MFCS.2018.36},
annote = {Keywords: temporal graph exploration, algorithmic graph theory, NP-complete problem}
}
Document
Approximating Dominating Set on Intersection Graphs of Rectangles and L-frames
Abstract
We consider the Minimum Dominating Set (MDS) problem on the intersection graphs of geometric objects. Even for simple and widely-used geometric objects such as rectangles, no sub-logarithmic approximation is known for the problem and (perhaps surprisingly) the problem is NP-hard even when all the rectangles are "anchored" at a diagonal line with slope -1 (Pandit, CCCG 2017). In this paper, we first show that for any epsilon>0, there exists a (2+epsilon)-approximation algorithm for the MDS problem on "diagonal-anchored" rectangles, providing the first O(1)-approximation for the problem on a non-trivial subclass of rectangles. It is not hard to see that the MDS problem on "diagonal-anchored" rectangles is the same as the MDS problem on "diagonal-anchored" L-frames: the union of a vertical and a horizontal line segment that share an endpoint. As such, we also obtain a (2+epsilon)-approximation for the problem with "diagonal-anchored" L-frames. On the other hand, we show that the problem is APX-hard in case the input L-frames intersect the diagonal, or the horizontal segments of the L-frames intersect a vertical line. However, as we show, the problem is linear-time solvable in case the L-frames intersect a vertical as well as a horizontal line. Finally, we consider the MDS problem in the so-called "edge intersection model" and obtain a number of results, answering two questions posed by Mehrabi (WAOA 2017).
Cite as
Sayan Bandyapadhyay, Anil Maheshwari, Saeed Mehrabi, and Subhash Suri. Approximating Dominating Set on Intersection Graphs of Rectangles and L-frames. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{bandyapadhyay_et_al:LIPIcs.MFCS.2018.37,
author = {Bandyapadhyay, Sayan and Maheshwari, Anil and Mehrabi, Saeed and Suri, Subhash},
title = {{Approximating Dominating Set on Intersection Graphs of Rectangles and L-frames}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {37:1--37:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.37},
URN = {urn:nbn:de:0030-drops-96198},
doi = {10.4230/LIPIcs.MFCS.2018.37},
annote = {Keywords: Minimum dominating set, Rectangles and L-frames, Approximation schemes, Local search, APX-hardness}
}
Document
On Efficiently Solvable Cases of Quantum k-SAT
Abstract
The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k >= 3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been well-studied for special tractable cases, as well as from a parameterized complexity perspective, much less is known in similar settings for k-QSAT. Here, we study the open problem of computing satisfying assignments to k-QSAT instances which have a "matching" or "dimer covering"; this is an NP problem whose decision variant is trivial, but whose search complexity remains open.
Our results fall into three directions, all of which relate to the "matching" setting: (1) We give a polynomial-time classical algorithm for k-QSAT when all qubits occur in at most two clauses. (2) We give a parameterized algorithm for k-QSAT instances from a certain non-trivial class, which allows us to obtain exponential speedups over brute force methods in some cases by reducing the problem to solving for a single root of a single univariate polynomial. (3) We conduct a structural graph theoretic study of 3-QSAT interaction graphs which have a "matching". We remark that the results of (2), in particular, introduce a number of new tools to the study of Quantum SAT, including graph theoretic concepts such as transfer filtrations and blow-ups from algebraic geometry; we hope these prove useful elsewhere.
Cite as
Marco Aldi, Niel de Beaudrap, Sevag Gharibian, and Seyran Saeedi. On Efficiently Solvable Cases of Quantum k-SAT. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{aldi_et_al:LIPIcs.MFCS.2018.38,
author = {Aldi, Marco and de Beaudrap, Niel and Gharibian, Sevag and Saeedi, Seyran},
title = {{On Efficiently Solvable Cases of Quantum k-SAT}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {38:1--38:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.38},
URN = {urn:nbn:de:0030-drops-96201},
doi = {10.4230/LIPIcs.MFCS.2018.38},
annote = {Keywords: search complexity, local Hamiltonian, Quantum SAT, algebraic geometry}
}
Document
Balanced Connected Partitioning of Unweighted Grid Graphs
Abstract
We consider a partitioning problem for grid graphs with special constraints: a (square) grid graph as well as a number of colors is given, a solution is a coloring approximatively assigning the same number of vertices to each color and such that the induced subgraph for each color is connected. In a "rooted" variant, a vertex to be included in the coloring for each color is specified as well. This problem has a concrete motivation in multimedia streaming applications.
We show that the general problem is NP-complete. On the other hand, we define a reasonable easy subclass of grid graphs for which solutions always exist and can be computed by a greedy algorithm.
Cite as
Cedric Berenger, Peter Niebert, and Kevin Perrot. Balanced Connected Partitioning of Unweighted Grid Graphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 39:1-39:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{berenger_et_al:LIPIcs.MFCS.2018.39,
author = {Berenger, Cedric and Niebert, Peter and Perrot, Kevin},
title = {{Balanced Connected Partitioning of Unweighted Grid Graphs}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {39:1--39:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.39},
URN = {urn:nbn:de:0030-drops-96213},
doi = {10.4230/LIPIcs.MFCS.2018.39},
annote = {Keywords: grid graphs, connected partitioning, NP-completeness, graph algorithm}
}
Document
Concurrent Games and Semi-Random Determinacy
Abstract
Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of winning (finite-memory) strategies in finitely many derived one-player games. Several classical winning conditions satisfy this simple requirement.
Under an additional requirement on the winning condition, the non-existence of Player 1 winning strategies from all vertices is equivalent to the existence of Player 2 stochastic strategies almost-sure winning from all vertices. Only few classical winning conditions satisfy this additional requirement, but a fairness variant of omega-regular languages does.
Cite as
Stéphane Le Roux. Concurrent Games and Semi-Random Determinacy. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 40:1-40:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{leroux:LIPIcs.MFCS.2018.40,
author = {Le Roux, St\'{e}phane},
title = {{Concurrent Games and Semi-Random Determinacy}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {40:1--40:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.40},
URN = {urn:nbn:de:0030-drops-96220},
doi = {10.4230/LIPIcs.MFCS.2018.40},
annote = {Keywords: Two-player win/lose, graph, infinite duration, abstract winning condition}
}
Document
Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations
Abstract
Low rank approximation of matrices is an important tool in machine learning. Given a data matrix, low rank approximation helps to find factors, patterns, and provides concise representations for the data. Research on low rank approximation usually focuses on real matrices. However, in many applications data are binary (categorical) rather than continuous. This leads to the problem of low rank approximation of binary matrices. Here we are given a d x n binary matrix A and a small integer k < d. The goal is to find two binary matrices U and V of sizes d x k and k x n respectively, so that the Frobenius norm of A - U V is minimized. There are two models of this problem, depending on the definition of the dot product of binary vectors: The GF(2) model and the Boolean semiring model. Unlike low rank approximation of a real matrix which can be efficiently solved by Singular Value Decomposition, we show that approximation of a binary matrix is NP-hard, even for k=1.
In this paper, our main concern is the problem of Column Subset Selection (CSS), in which the low rank matrix U must be formed by k columns of the data matrix, and we are interested in the approximation ratio achievable by CSS for binary matrices. For the GF(2) model, we show that CSS has approximation ratio bounded by k/2+1+k/(2(2^k-1)) and this is asymptotically tight. For the Boolean model, it turns out that CSS is no longer sufficient to obtain a bound. We then develop a Generalized CSS (GCSS) procedure in which the columns of U are generated from Boolean formulas operating bitwise on selected columns of the data matrix. We show that the approximation ratio achieved by GCSS is bounded by 2^(k-1)+1, and argue that an exponential dependency on k is seems inherent.
Cite as
Chen Dan, Kristoffer Arnsfelt Hansen, He Jiang, Liwei Wang, and Yuchen Zhou. Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 41:1-41:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{dan_et_al:LIPIcs.MFCS.2018.41,
author = {Dan, Chen and Hansen, Kristoffer Arnsfelt and Jiang, He and Wang, Liwei and Zhou, Yuchen},
title = {{Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {41:1--41:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.41},
URN = {urn:nbn:de:0030-drops-96239},
doi = {10.4230/LIPIcs.MFCS.2018.41},
annote = {Keywords: Approximation Algorithms, Low Rank Approximation, Binary Matrices}
}
Document
Optimal Strategies in Pushdown Reachability Games
Abstract
An algorithm for computing optimal strategies in pushdown reachability games was given by Cachat. We show that the information tracked by this algorithm is too coarse and the strategies constructed are not necessarily optimal. We then show that the algorithm can be refined to recover optimality. Through a further non-trivial argument the refined algorithm can be run in 2EXPTIME by bounding the play-lengths tracked to those that are at most doubly exponential. This is optimal in the sense that there exists a game for which the optimal strategy requires a doubly exponential number of moves to reach a target configuration.
Cite as
Arnaud Carayol and Matthew Hague. Optimal Strategies in Pushdown Reachability Games. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{carayol_et_al:LIPIcs.MFCS.2018.42,
author = {Carayol, Arnaud and Hague, Matthew},
title = {{Optimal Strategies in Pushdown Reachability Games}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {42:1--42:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.42},
URN = {urn:nbn:de:0030-drops-96248},
doi = {10.4230/LIPIcs.MFCS.2018.42},
annote = {Keywords: Pushdown Systems, Reachability Games, Optimal Strategies, Formal Methods, Context Free}
}
Document
Why are CSPs Based on Partition Schemes Computationally Hard?
Abstract
Many computational problems arising in, for instance, artificial intelligence can be realized as infinite-domain constraint satisfaction problems (CSPs) based on partition schemes: a set of pairwise disjoint binary relations (containing the equality relation) whose union spans the underlying domain and which is closed under converse. We first consider partition schemes that contain a strict partial order and where the constraint language contains all unions of the basic relations; such CSPs are frequently occurring in e.g. temporal and spatial reasoning. We identify three properties of such orders which, when combined, are sufficient to establish NP-hardness of the CSP. This result explains, in a uniform way, many existing hardness results from the literature. More importantly, this result enables us to prove that CSPs of this kind are not solvable in subexponential time unless the exponential-time hypothesis (ETH) fails. We continue by studying constraint languages based on partition schemes but where relations are built using disjunctions instead of unions; such CSPs appear naturally when analysing first-order definable constraint languages. We prove that such CSPs are NP-hard even in very restricted settings and that they are not solvable in subexponential time under the randomised ETH. In certain cases, we can additionally show that they cannot be solved in O(c^n) time for any c >= 0.
Cite as
Peter Jonsson and Victor Lagerkvist. Why are CSPs Based on Partition Schemes Computationally Hard?. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{jonsson_et_al:LIPIcs.MFCS.2018.43,
author = {Jonsson, Peter and Lagerkvist, Victor},
title = {{Why are CSPs Based on Partition Schemes Computationally Hard?}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {43:1--43:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.43},
URN = {urn:nbn:de:0030-drops-96257},
doi = {10.4230/LIPIcs.MFCS.2018.43},
annote = {Keywords: Constraint satisfaction problems, infinite domains, partition schemes, lower bounds}
}
Document
Directed Graph Minors and Serial-Parallel Width
Abstract
Graph minors are a primary tool in understanding the structure of undirected graphs, with many conceptual and algorithmic implications. We propose new variants of directed graph minors and directed graph embeddings, by modifying familiar definitions. For the class of 2-terminal directed acyclic graphs (TDAGs) our two definitions coincide, and the class is closed under both operations. The usefulness of our directed minor operations is demonstrated by characterizing all TDAGs with serial-parallel width at most k; a class of networks known to guarantee bounded negative externality in nonatomic routing games. Our characterization implies that a TDAG has serial-parallel width of 1 if and only if it is a directed series-parallel graph. We also study the computational complexity of finding a directed minor and computing the serial-parallel width.
Cite as
Argyrios Deligkas and Reshef Meir. Directed Graph Minors and Serial-Parallel Width. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{deligkas_et_al:LIPIcs.MFCS.2018.44,
author = {Deligkas, Argyrios and Meir, Reshef},
title = {{Directed Graph Minors and Serial-Parallel Width}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {44:1--44:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.44},
URN = {urn:nbn:de:0030-drops-96261},
doi = {10.4230/LIPIcs.MFCS.2018.44},
annote = {Keywords: directed minors, pathwidth}
}
Document
The Complexity of Finding Small Separators in Temporal Graphs
Abstract
Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths connecting one terminal to the other. Herein, we consider two models of temporal paths: paths that pass through arbitrarily many edges per time step (non-strict) and paths that pass through at most one edge per time step (strict). Regarding the number of time steps of a temporal graph, we show a complexity dichotomy (NP-hardness versus polynomial-time solvability) for both problem variants. Moreover we prove both problem variants to be NP-complete even on temporal graphs whose underlying graph is planar. We further show that, on temporal graphs with planar underlying graph, if additionally the number of time steps is constant, then the problem variant for strict paths is solvable in quasi-linear time. Finally, we introduce and motivate the notion of a temporal core (vertices whose incident edges change over time). We prove that the non-strict variant is fixed-parameter tractable when parameterized by the size of the temporal core, while the strict variant remains NP-complete, even for constant-size temporal cores.
Cite as
Philipp Zschoche, Till Fluschnik, Hendrik Molter, and Rolf Niedermeier. The Complexity of Finding Small Separators in Temporal Graphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 45:1-45:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{zschoche_et_al:LIPIcs.MFCS.2018.45,
author = {Zschoche, Philipp and Fluschnik, Till and Molter, Hendrik and Niedermeier, Rolf},
title = {{The Complexity of Finding Small Separators in Temporal Graphs}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {45:1--45:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.45},
URN = {urn:nbn:de:0030-drops-96277},
doi = {10.4230/LIPIcs.MFCS.2018.45},
annote = {Keywords: (non-)strict temporal paths, temporal core, single-source shortest paths, node multiway cut, length-bounded cuts, parameterized complexity}
}
Document
The Complexity of Transducer Synthesis from Multi-Sequential Specifications
Abstract
The transducer synthesis problem on finite words asks, given a specification S subseteq I x O, where I and O are sets of finite words, whether there exists an implementation f: I - > O which (1) fulfils the specification, i.e., (i,f(i))in S for all i in I, and (2) can be defined by some input-deterministic (aka sequential) transducer T_f. If such an implementation f exists, the procedure should also output T_f. The realisability problem is the corresponding decision problem.
For specifications given by synchronous transducers (which read and write alternately one symbol), this is the finite variant of the classical synthesis problem on omega-words, solved by Büchi and Landweber in 1969, and the realisability problem is known to be ExpTime-c in both finite and omega-word settings. For specifications given by asynchronous transducers (which can write a batch of symbols, or none, in a single step), the realisability problem is known to be undecidable.
We consider here the class of multi-sequential specifications, defined as finite unions of sequential transducers over possibly incomparable domains. We provide optimal decision procedures for the realisability problem in both the synchronous and asynchronous setting, showing that it is PSpace-c. Moreover, whenever the specification is realisable, we expose the construction of a sequential transducer that realises it and has a size that is doubly exponential, which we prove to be optimal.
Cite as
Léo Exibard, Emmanuel Filiot, and Ismaël Jecker. The Complexity of Transducer Synthesis from Multi-Sequential Specifications. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{exibard_et_al:LIPIcs.MFCS.2018.46,
author = {Exibard, L\'{e}o and Filiot, Emmanuel and Jecker, Isma\"{e}l},
title = {{The Complexity of Transducer Synthesis from Multi-Sequential Specifications}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {46:1--46:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.46},
URN = {urn:nbn:de:0030-drops-96286},
doi = {10.4230/LIPIcs.MFCS.2018.46},
annote = {Keywords: Transducers, Multi-Sequentiality, Synthesis}
}
Document
Pricing Problems with Buyer Preselection
Abstract
We investigate the problem of preselecting a subset of buyers participating in a market so as to optimize the performance of stable outcomes. We consider four scenarios arising from the combination of two stability notions, item and bundle envy-freeness, with the two classical objective functions, i.e., the social welfare and the seller's revenue. When adopting the notion of item envy-freeness, we prove that, for both the two objective functions, the problem cannot be approximated within n^(1-epsilon) for any epsilon >0, and provide tight or nearly tight approximation algorithms. We also prove that maximizing the seller's revenue is NP-hard even for a single buyer, thus closing an open question. Under bundle envy-freeness, instead, we show how to transform in polynomial time any stable outcome for a market involving only a subset of buyers to a stable one for the whole market without worsening its performance, both for the social welfare and the seller's revenue. Finally, we consider multi-unit markets, where all items are of the same type and are assigned the same price. For this specific case, we show that buyer preselection can improve the performance of stable outcomes in all of the four considered scenarios, and we design corresponding approximation algorithms.
Cite as
Vittorio Bilò, Michele Flammini, Gianpiero Monaco, and Luca Moscardelli. Pricing Problems with Buyer Preselection. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{bilo_et_al:LIPIcs.MFCS.2018.47,
author = {Bil\`{o}, Vittorio and Flammini, Michele and Monaco, Gianpiero and Moscardelli, Luca},
title = {{Pricing Problems with Buyer Preselection}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {47:1--47:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.47},
URN = {urn:nbn:de:0030-drops-96292},
doi = {10.4230/LIPIcs.MFCS.2018.47},
annote = {Keywords: Pricing problems, Envy-freeness, Revenue maximization, Social Welfare maximization}
}
Document
On Randomized Generation of Slowly Synchronizing Automata
Abstract
Motivated by the randomized generation of slowly synchronizing automata, we study automata made of permutation letters and a merging letter of rank n-1 . We present a constructive randomized procedure to generate synchronizing automata of that kind with (potentially) large alphabet size based on recent results on primitive sets of matrices. We report numerical results showing that our algorithm finds automata with much larger reset threshold than a mere uniform random generation and we present new families of automata with reset threshold of Omega(n^2/4) . We finally report theoretical results on randomized generation of primitive sets of matrices: a set of permutation matrices with a 0 entry changed into a 1 is primitive and has exponent of O(n log n) with high probability in case of uniform random distribution and the same holds for a random set of binary matrices where each entry is set, independently, equal to 1 with probability p and equal to 0 with probability 1-p , when np-log n - > infty as n - > infty .
Cite as
Costanza Catalano and Raphaël M. Jungers. On Randomized Generation of Slowly Synchronizing Automata. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{catalano_et_al:LIPIcs.MFCS.2018.48,
author = {Catalano, Costanza and Jungers, Rapha\"{e}l M.},
title = {{On Randomized Generation of Slowly Synchronizing Automata}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {48:1--48:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.48},
URN = {urn:nbn:de:0030-drops-96305},
doi = {10.4230/LIPIcs.MFCS.2018.48},
annote = {Keywords: Synchronizing automata, random automata, Cern\'{y} conjecture, automata with simple idempotents, primitive sets of matrices}
}
Document
Counting Homomorphisms to Trees Modulo a Prime
Abstract
Many important graph theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular independent sets and colourings. In this article we study the complexity of #_pHomsToH, the problem of counting graph homomorphisms from an input graph to a graph H modulo a prime number p. Dyer and Greenhill proved a dichotomy stating that the tractability of non-modular counting graph homomorphisms depends on the structure of the target graph. Many intractable cases in non-modular counting become tractable in modular counting due to the common phenomenon of cancellation. In subsequent studies on counting modulo 2, however, the influence of the structure of H on the tractability was shown to persist, which yields similar dichotomies.
Our main result states that for every tree H and every prime p the problem #_pHomsToH is either polynomial time computable or #_pP-complete. This relates to the conjecture of Faben and Jerrum stating that this dichotomy holds for every graph H when counting modulo 2. In contrast to previous results on modular counting, the tractable cases of #_pHomsToH are essentially the same for all values of the modulo when H is a tree. To prove this result, we study the structural properties of a homomorphism. As an important interim result, our study yields a dichotomy for the problem of counting weighted independent sets in a bipartite graph modulo some prime p. These results are the first suggesting that such dichotomies hold not only for the one-bit functions of the modulo 2 case but also for the modular counting functions of all primes p.
Cite as
Andreas Göbel, J. A. Gregor Lagodzinski, and Karen Seidel. Counting Homomorphisms to Trees Modulo a Prime. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 49:1-49:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{gobel_et_al:LIPIcs.MFCS.2018.49,
author = {G\"{o}bel, Andreas and Lagodzinski, J. A. Gregor and Seidel, Karen},
title = {{Counting Homomorphisms to Trees Modulo a Prime}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {49:1--49:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.49},
URN = {urn:nbn:de:0030-drops-96315},
doi = {10.4230/LIPIcs.MFCS.2018.49},
annote = {Keywords: Algorithms, Theory, Graph Homomorphisms, Counting Modulo a Prime, Complexity Dichotomy}
}
Document
Car-Sharing between Two Locations: Online Scheduling with Two Servers
Abstract
In this paper, we consider an on-line scheduling problem that is motivated by applications such as car sharing, in which users submit ride requests, and the scheduler aims to accept requests of maximum total profit using two servers (cars). Each ride request specifies the pick-up time and the pick-up location (among two locations, with the other location being the destination). The length of the time interval between the submission of a request (booking time) and the pick-up time is fixed. The scheduler has to decide whether or not to accept a request immediately at the time when the request is submitted. We present lower bounds on the competitive ratio for this problem and propose a smart greedy algorithm that achieves the best possible competitive ratio.
Cite as
Kelin Luo, Thomas Erlebach, and Yinfeng Xu. Car-Sharing between Two Locations: Online Scheduling with Two Servers. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{luo_et_al:LIPIcs.MFCS.2018.50,
author = {Luo, Kelin and Erlebach, Thomas and Xu, Yinfeng},
title = {{Car-Sharing between Two Locations: Online Scheduling with Two Servers}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {50:1--50:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.50},
URN = {urn:nbn:de:0030-drops-96325},
doi = {10.4230/LIPIcs.MFCS.2018.50},
annote = {Keywords: Car-sharing system, Competitive analysis, On-line scheduling}
}
Document
The Robustness of LWPP and WPP, with an Application to Graph Reconstruction
Abstract
We show that the counting class LWPP [S. Fenner et al., 1994] remains unchanged even if one allows a polynomial number of gap values rather than one. On the other hand, we show that it is impossible to improve this from polynomially many gap values to a superpolynomial number of gap values by relativizable proof techniques.
The first of these results implies that the Legitimate Deck Problem (from the study of graph reconstruction) is in LWPP (and thus low for PP, i.e., PP^{Legitimate Deck} = PP) if the weakened version of the Reconstruction Conjecture holds in which the number of nonisomorphic preimages is assumed merely to be polynomially bounded. This strengthens the 1992 result of Köbler, Schöning, and Torán [J. Köbler et al., 1992] that the Legitimate Deck Problem is in LWPP if the Reconstruction Conjecture holds, and provides strengthened evidence that the Legitimate Deck Problem is not NP-hard.
We additionally show on the one hand that our main LWPP robustness result also holds for WPP, and also holds even when one allows both the rejection- and acceptance- gap-value targets to simultaneously be polynomial-sized lists; yet on the other hand, we show that for the #P-based analog of LWPP the behavior much differs in that, in some relativized worlds, even two target values already yield a richer class than one value does.
Cite as
Edith Hemaspaandra, Lane A. Hemaspaandra, Holger Spakowski, and Osamu Watanabe. The Robustness of LWPP and WPP, with an Application to Graph Reconstruction. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 51:1-51:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{hemaspaandra_et_al:LIPIcs.MFCS.2018.51,
author = {Hemaspaandra, Edith and Hemaspaandra, Lane A. and Spakowski, Holger and Watanabe, Osamu},
title = {{The Robustness of LWPP and WPP, with an Application to Graph Reconstruction}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {51:1--51:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.51},
URN = {urn:nbn:de:0030-drops-96330},
doi = {10.4230/LIPIcs.MFCS.2018.51},
annote = {Keywords: structural complexity theory, robustness of counting classes, the legitimate deck problem, PP-lowness, the Reconstruction Conjecture}
}
Document
Shape Recognition by a Finite Automaton Robot
Abstract
Motivated by the problem of shape recognition by nanoscale computing agents, we investigate the problem of detecting the geometric shape of a structure composed of hexagonal tiles by a finite-state automaton robot. In particular, in this paper we consider the question of recognizing whether the tiles are assembled into a parallelogram whose longer side has length l = f(h), for a given function f(*), where h is the length of the shorter side. To determine the computational power of the finite-state automaton robot, we identify functions that can or cannot be decided when the robot is given a certain number of pebbles. We show that the robot can decide whether l = ah+b for constant integers a and b without any pebbles, but cannot detect whether l = f(h) for any function f(x) = omega(x). For a robot with a single pebble, we present an algorithm to decide whether l = p(h) for a given polynomial p(*) of constant degree. We contrast this result by showing that, for any constant k, any function f(x) = omega(x^(6k + 2)) cannot be decided by a robot with k states and a single pebble. We further present exponential functions that can be decided using two pebbles. Finally, we present a family of functions f_n(*) such that the robot needs more than n pebbles to decide whether l = f_n(h).
Cite as
Robert Gmyr, Kristian Hinnenthal, Irina Kostitsyna, Fabian Kuhn, Dorian Rudolph, and Christian Scheideler. Shape Recognition by a Finite Automaton Robot. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{gmyr_et_al:LIPIcs.MFCS.2018.52,
author = {Gmyr, Robert and Hinnenthal, Kristian and Kostitsyna, Irina and Kuhn, Fabian and Rudolph, Dorian and Scheideler, Christian},
title = {{Shape Recognition by a Finite Automaton Robot}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {52:1--52:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.52},
URN = {urn:nbn:de:0030-drops-96347},
doi = {10.4230/LIPIcs.MFCS.2018.52},
annote = {Keywords: finite automata, shape recognition, computational geometry}
}
Document
Conflict Free Feedback Vertex Set: A Parameterized Dichotomy
Abstract
In this paper we study recently introduced conflict version of the classical Feedback Vertex Set (FVS) problem. For a family of graphs F, we consider the problem F-CF-Feedback Vertex Set (F-CF-FVS, for short). The F-CF-FVS problem takes as an input a graph G, a graph H in F (where V(G)=V(H)), and an integer k, and the objective is to decide if there is a set S subseteq V(G) of size at most k such that G-S is a forest and S is an independent set in H. Observe that if we instantiate F to be the family of edgeless graphs then we get the classical FVS problem. Jain, Kanesh, and Misra [CSR 2018] showed that in contrast to FVS, F-CF-FVS is W[1]-hard on general graphs and admits an FPT algorithm if F is the family of d-degenerate graphs. In this paper, we relate F-CF-FVS to the Independent Set problem on special classes of graphs, and obtain a complete dichotomy result on the Parameterized Complexity of the problem F-CF-FVS, when F is a hereditary graph family. In particular, we show that F-CF-FVS is FPT parameterized by the solution size if and only if F+Cluster IS is FPT parameterized by the solution size. Here, F+Cluster IS is the Independent Set problem in the (edge) union of a graph G in F and a cluster graph H (G and H are explicitly given). Next, we exploit this characterization to obtain new FPT results as well as intractability results for F-CF-FVS. In particular, we give an FPT algorithm for F+Cluster IS when F is the family of K_{i,j}-free graphs. We show that for the family of bipartite graph B, B-CF-FVS is W[1]-hard, when parameterized by the solution size. Finally, we consider, for each 0< epsilon<1, the family of graphs F_epsilon, which comprise of graphs G such that |E(G)| <= |V(G)|^(2-epsilon), and show that F_epsilon-CF-FVS is W[1]-hard, when parameterized by the solution size, for every 0<epsilon<1.
Cite as
Akanksha Agrawal, Pallavi Jain, Lawqueen Kanesh, Daniel Lokshtanov, and Saket Saurabh. Conflict Free Feedback Vertex Set: A Parameterized Dichotomy. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 53:1-53:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{agrawal_et_al:LIPIcs.MFCS.2018.53,
author = {Agrawal, Akanksha and Jain, Pallavi and Kanesh, Lawqueen and Lokshtanov, Daniel and Saurabh, Saket},
title = {{Conflict Free Feedback Vertex Set: A Parameterized Dichotomy}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {53:1--53:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.53},
URN = {urn:nbn:de:0030-drops-96355},
doi = {10.4230/LIPIcs.MFCS.2018.53},
annote = {Keywords: Conflict-free, Feedback Vertex Set, FPT algorithm, W\lbrack1\rbrack-hardness}
}
Document
Largest Weight Common Subtree Embeddings with Distance Penalties
Abstract
The largest common embeddable subtree problem asks for the largest possible tree embeddable into two input trees and generalizes the classical maximum common subtree problem. Several variants of the problem in labeled and unlabeled rooted trees have been studied, e.g., for the comparison of evolutionary trees. We consider a generalization, where the sought embedding is maximal with regard to a weight function on pairs of labels. We support rooted and unrooted trees with vertex and edge labels as well as distance penalties for skipping vertices. This variant is important for many applications such as the comparison of chemical structures and evolutionary trees. Our algorithm computes the solution from a series of bipartite matching instances, which are solved efficiently by exploiting their structural relation and imbalance. Our analysis shows that our approach improves or matches the running time of the formally best algorithms for several problem variants. Specifically, we obtain a running time of O(|T| |T'|Delta) for two rooted or unrooted trees T and T', where Delta=min{Delta(T),Delta(T')} with Delta(X) the maximum degree of X. If the weights are integral and at most C, we obtain a running time of O(|T| |T'|sqrt Delta log (C min{|T|,|T'|})) for rooted trees.
Cite as
Andre Droschinsky, Nils M. Kriege, and Petra Mutzel. Largest Weight Common Subtree Embeddings with Distance Penalties. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 54:1-54:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{droschinsky_et_al:LIPIcs.MFCS.2018.54,
author = {Droschinsky, Andre and Kriege, Nils M. and Mutzel, Petra},
title = {{Largest Weight Common Subtree Embeddings with Distance Penalties}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {54:1--54:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.54},
URN = {urn:nbn:de:0030-drops-96367},
doi = {10.4230/LIPIcs.MFCS.2018.54},
annote = {Keywords: maximum common subtree, largest embeddable subtree, topological embedding, maximum weight matching, subtree homeomorphism}
}
Document
Enumerating Minimal Transversals of Hypergraphs without Small Holes
Abstract
We give a polynomial delay algorithm for enumerating the minimal transversals of hypergraphs without induced cycles of length 3 and 4. As a corollary, we can enumerate, with polynomial delay, the vertices of any polyhedron P(A,1)={x in R^n | Ax >= 1, x >= 0}, when A is a balanced matrix that does not contain as a submatrix the incidence matrix of a cycle of length 4. Other consequences are a polynomial delay algorithm for enumerating the minimal dominating sets of graphs of girth at least 9 and an incremental delay algorithm for enumerating all the minimal dominating sets of a bipartite graph without induced 6 and 8-cycles.
Cite as
Mamadou M. Kanté, Kaveh Khoshkhah, and Mozhgan Pourmoradnasseri. Enumerating Minimal Transversals of Hypergraphs without Small Holes. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{kante_et_al:LIPIcs.MFCS.2018.55,
author = {Kant\'{e}, Mamadou M. and Khoshkhah, Kaveh and Pourmoradnasseri, Mozhgan},
title = {{Enumerating Minimal Transversals of Hypergraphs without Small Holes}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {55:1--55:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.55},
URN = {urn:nbn:de:0030-drops-96372},
doi = {10.4230/LIPIcs.MFCS.2018.55},
annote = {Keywords: Triangle-free Hypergraph, Minimal Transversal, Balanced Matrix, Minimal Dominating Set}
}
Document
Collective Fast Delivery by Energy-Efficient Agents
Abstract
We consider k mobile agents initially located at distinct nodes of an undirected graph (on n nodes, with edge lengths). The agents have to deliver a single item from a given source node s to a given target node t. The agents can move along the edges of the graph, starting at time 0, with respect to the following: Each agent i has a weight omega_i that defines the rate of energy consumption while travelling a distance in the graph, and a velocity upsilon_i with which it can move.
We are interested in schedules (operating the k agents) that result in a small delivery time T (time when the item arrives at t), and small total energy consumption E. Concretely, we ask for a schedule that: either (i) Minimizes T, (ii) Minimizes lexicographically (T,E) (prioritizing fast delivery), or (iii) Minimizes epsilon * T + (1-epsilon)* E, for a given epsilon in (0,1).
We show that (i) is solvable in polynomial time, and show that (ii) is polynomial-time solvable for uniform velocities and solvable in time O(n+k log k) for arbitrary velocities on paths, but in general is NP-hard even on planar graphs. As a corollary of our hardness result, (iii) is NP-hard, too. We show that there is a 2-approximation algorithm for (iii) using a single agent.
Cite as
Andreas Bärtschi, Daniel Graf, and Matús Mihalák. Collective Fast Delivery by Energy-Efficient Agents. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 56:1-56:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{bartschi_et_al:LIPIcs.MFCS.2018.56,
author = {B\"{a}rtschi, Andreas and Graf, Daniel and Mihal\'{a}k, Mat\'{u}s},
title = {{Collective Fast Delivery by Energy-Efficient Agents}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {56:1--56:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.56},
URN = {urn:nbn:de:0030-drops-96381},
doi = {10.4230/LIPIcs.MFCS.2018.56},
annote = {Keywords: delivery, mobile agents, time/energy optimization, complexity, algorithms}
}
Document
Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Systems
Abstract
We give a direct polynomial-time reduction from parity games played over the configuration graphs of collapsible pushdown systems to safety games played over the same class of graphs. That a polynomial-time reduction would exist was known since both problems are complete for the same complexity class. Coming up with a direct reduction, however, has been an open problem. Our solution to the puzzle brings together a number of techniques for pushdown games and adds three new ones. This work contributes to a recent trend of liveness to safety reductions which allow the advanced state-of-the-art in safety checking to be used for more expressive specifications.
Cite as
Matthew Hague, Roland Meyer, Sebastian Muskalla, and Martin Zimmermann. Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Systems. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 57:1-57:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{hague_et_al:LIPIcs.MFCS.2018.57,
author = {Hague, Matthew and Meyer, Roland and Muskalla, Sebastian and Zimmermann, Martin},
title = {{Parity to Safety in Polynomial Time for Pushdown and Collapsible Pushdown Systems}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {57:1--57:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.57},
URN = {urn:nbn:de:0030-drops-96396},
doi = {10.4230/LIPIcs.MFCS.2018.57},
annote = {Keywords: Parity Games, Safety Games, Pushdown Systems, Collapsible Pushdown Systems, Higher-Order Recursion Schemes, Model Checking}
}
Document
Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2)
Abstract
The polynomial-time hierarchy (PH) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as PH does not collapse). Here, we study whether two quantum generalizations of PH can similarly prove separations in the quantum setting. The first generalization, QCPH, uses classical proofs, and the second, QPH, uses quantum proofs. For the former, we show quantum variants of the Karp-Lipton theorem and Toda's theorem. For the latter, we place its third level, Q Sigma_3, into NEXP using the Ellipsoid Method for efficiently solving semidefinite programs. These results yield two implications for QMA(2), the variant of Quantum Merlin-Arthur (QMA) with two unentangled proofs, a complexity class whose characterization has proven difficult. First, if QCPH=QPH (i.e., alternating quantifiers are sufficiently powerful so as to make classical and quantum proofs "equivalent"), then QMA(2) is in the Counting Hierarchy (specifically, in P^{PP^{PP}}). Second, unless QMA(2)= Q Sigma_3 (i.e., alternating quantifiers do not help in the presence of "unentanglement"), QMA(2) is strictly contained in NEXP.
Cite as
Sevag Gharibian, Miklos Santha, Jamie Sikora, Aarthi Sundaram, and Justin Yirka. Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2). In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 58:1-58:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{gharibian_et_al:LIPIcs.MFCS.2018.58,
author = {Gharibian, Sevag and Santha, Miklos and Sikora, Jamie and Sundaram, Aarthi and Yirka, Justin},
title = {{Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2)}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {58:1--58:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.58},
URN = {urn:nbn:de:0030-drops-96409},
doi = {10.4230/LIPIcs.MFCS.2018.58},
annote = {Keywords: Complexity Theory, Quantum Computing, Polynomial Hierarchy, Semidefinite Programming, QMA(2), Quantum Complexity}
}
Document
A Subquadratic Algorithm for 3XOR
Abstract
Given a set X of n binary words of equal length w, the 3XOR problem asks for three elements a, b, c in X such that a oplus b=c, where oplus denotes the bitwise XOR operation. The problem can be easily solved on a word RAM with word length w in time O(n^2 log n). Using Han's fast integer sorting algorithm (STOC/J. Algorithms, 2002/2004) this can be reduced to O(n^2 log log n). With randomization or a sophisticated deterministic dictionary construction, creating a hash table for X with constant lookup time leads to an algorithm with (expected) running time O(n^2). At present, seemingly no faster algorithms are known.
We present a surprisingly simple deterministic, quadratic time algorithm for 3XOR. Its core is a version of the PATRICIA tree for X, which makes it possible to traverse the set a oplus X in ascending order for arbitrary a in {0, 1}^{w} in linear time. Furthermore, we describe a randomized algorithm for 3XOR with expected running time O(n^2 * min{log^3(w)/w, (log log n)^2/log^2 n}). The algorithm transfers techniques to our setting that were used by Baran, Demaine, and Patrascu (WADS/Algorithmica, 2005/2008) for solving the related int3SUM problem (the same problem with integer addition in place of binary XOR) in expected time o(n^2). As suggested by Jafargholi and Viola (Algorithmica, 2016), linear hash functions are employed.
The latter authors also showed that assuming 3XOR needs expected running time n^(2-o(1)) one can prove conditional lower bounds for triangle enumeration just as with 3SUM. We demonstrate that 3XOR can be reduced to other problems as well, treating the examples offline SetDisjointness and offline SetIntersection, which were studied for 3SUM by Kopelowitz, Pettie, and Porat (SODA, 2016).
Cite as
Martin Dietzfelbinger, Philipp Schlag, and Stefan Walzer. A Subquadratic Algorithm for 3XOR. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 59:1-59:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{dietzfelbinger_et_al:LIPIcs.MFCS.2018.59,
author = {Dietzfelbinger, Martin and Schlag, Philipp and Walzer, Stefan},
title = {{A Subquadratic Algorithm for 3XOR}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {59:1--59:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.59},
URN = {urn:nbn:de:0030-drops-96417},
doi = {10.4230/LIPIcs.MFCS.2018.59},
annote = {Keywords: 3SUM, 3XOR, Randomized Algorithms, Reductions, Conditional Lower Time Bounds}
}
Document
Treewidth-Two Graphs as a Free Algebra
Abstract
We give a new and elementary proof that the graphs of treewidth at most two can be seen as a free algebra. This result was originally established through an elaborate analysis of the structure of K_4-free graphs, ultimately reproving the well-known fact that the graphs of treewidth at most two are precisely those excluding K_4 as a minor. Our new proof is based on a confluent and terminating rewriting system for term-labeled graphs and does not involve graph minors anymore. The new strategy is simpler and robust in the sense that it can be adapted to subclasses of treewidth-two graphs, e.g., graphs without self-loops.
Cite as
Christian Doczkal and Damien Pous. Treewidth-Two Graphs as a Free Algebra. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 60:1-60:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{doczkal_et_al:LIPIcs.MFCS.2018.60,
author = {Doczkal, Christian and Pous, Damien},
title = {{Treewidth-Two Graphs as a Free Algebra}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {60:1--60:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.60},
URN = {urn:nbn:de:0030-drops-96429},
doi = {10.4230/LIPIcs.MFCS.2018.60},
annote = {Keywords: Treewidth, Universal Algebra, Rewriting}
}
Document
On Pseudodeterministic Approximation Algorithms
Abstract
We investigate the notion of pseudodeterminstic approximation algorithms. A randomized approximation algorithm A for a function f is pseudodeterministic if for every input x there is a unique value v so that A(x) outputs v with high probability, and v is a good approximation of f(x). We show that designing a pseudodeterministic version of Stockmeyer's well known approximation algorithm for the NP-membership counting problem will yield a new circuit lower bound: if such an approximation algorithm exists, then for every k, there is a language in the complexity class ZPP^{NP}_{tt} that does not have n^k-size circuits. While we do not know how to design such an algorithm for the NP-membership counting problem, we show a general result that any randomized approximation algorithm for a counting problem can be transformed to an approximation algorithm that has a constant number of influential random bits. That is, for most settings of these influential bits, the approximation algorithm will be pseudodeterministic.
Cite as
Peter Dixon, A. Pavan, and N. V. Vinodchandran. On Pseudodeterministic Approximation Algorithms. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 61:1-61:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{dixon_et_al:LIPIcs.MFCS.2018.61,
author = {Dixon, Peter and Pavan, A. and Vinodchandran, N. V.},
title = {{On Pseudodeterministic Approximation Algorithms}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {61:1--61:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.61},
URN = {urn:nbn:de:0030-drops-96431},
doi = {10.4230/LIPIcs.MFCS.2018.61},
annote = {Keywords: Approximation Algorithms, Circuit lower bounds, Pseudodeterminism}
}
Document
Testing Simon's congruence
Abstract
Piecewise testable languages are a subclass of the regular languages. There are many equivalent ways of defining them; Simon's congruence ~_k is one of the most classical approaches. Two words are ~_k-equivalent if they have the same set of (scattered) subwords of length at most k. A language L is piecewise testable if there exists some k such that L is a union of ~_k-classes.
For each equivalence class of ~_k, one can define a canonical representative in shortlex normal form, that is, the minimal word with respect to the lexicographic order among the shortest words in ~_k. We present an algorithm for computing the canonical representative of the ~_k-class of a given word w in A^* of length n. The running time of our algorithm is in O(|A| n) even if k <= n is part of the input. This is surprising since the number of possible subwords grows exponentially in k. The case k>n is not interesting since then, the equivalence class of w is a singleton. If the alphabet is fixed, the running time of our algorithm is linear in the size of the input word. Moreover, for fixed alphabet, we show that the computation of shortlex normal forms for ~_k is possible in deterministic logarithmic space.
One of the consequences of our algorithm is that one can check with the same complexity whether two words are ~_k-equivalent (with k being part of the input).
Cite as
Lukas Fleischer and Manfred Kufleitner. Testing Simon's congruence. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 62:1-62:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{fleischer_et_al:LIPIcs.MFCS.2018.62,
author = {Fleischer, Lukas and Kufleitner, Manfred},
title = {{Testing Simon's congruence}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {62:1--62:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.62},
URN = {urn:nbn:de:0030-drops-96445},
doi = {10.4230/LIPIcs.MFCS.2018.62},
annote = {Keywords: regular language, scattered subword, piecewise testability, string algorithm}
}
Document
On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal
Abstract
Let vc(G), fvs(G) and oct(G) denote, respectively, the size of a minimum vertex cover, minimum feedback vertex set and minimum odd cycle transversal in a graph G. One can ask, when looking for these sets in a graph, how much bigger might they be if we require that they are independent; that is, what is the price of independence? If G has a vertex cover, feedback vertex set or odd cycle transversal that is an independent set, then we let, respectively, ivc(G), ifvs(G) or ioct(G) denote the minimum size of such a set. We investigate for which graphs H the values of ivc(G), ifvs(G) and ioct(G) are bounded in terms of vc(G), fvs(G) and oct(G), respectively, when the graph G belongs to the class of H-free graphs. We find complete classifications for vertex cover and feedback vertex set and an almost complete classification for odd cycle transversal (subject to three non-equivalent open cases).
Cite as
Konrad K. Dabrowski, Matthew Johnson, Giacomo Paesani, Daniël Paulusma, and Viktor Zamaraev. On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 63:1-63:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{dabrowski_et_al:LIPIcs.MFCS.2018.63,
author = {Dabrowski, Konrad K. and Johnson, Matthew and Paesani, Giacomo and Paulusma, Dani\"{e}l and Zamaraev, Viktor},
title = {{On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {63:1--63:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.63},
URN = {urn:nbn:de:0030-drops-96452},
doi = {10.4230/LIPIcs.MFCS.2018.63},
annote = {Keywords: vertex cover, feedback vertex set, odd cycle transversal, price of independence}
}
Document
Probabilistic Secret Sharing
Abstract
In classical secret sharing schemes a dealer shares a secret among a set of participants in such a way that qualified subsets can reconstruct the secret, while forbidden ones do not get any kind of information about it. The basic parameter to optimize is the size of the shares, that is, the amount of secret information that the dealer has to give to participants. In this paper we formalize a notion of probabilistic secret sharing schemes, in which qualified subsets can reconstruct the secret but only with a certain controlled probability. We show that, by allowing a bounded error in the reconstruction of the secret, it is possible to drastically reduce the size of the shares the participants get (with respect to classical secret sharing schemes). We provide efficient constructions both for threshold access structures on a finite set of participants and for evolving threshold access structures, where the set of participants is potentially infinite. Some of our constructions yield shares of constant size (i.e., not depending on the number of participants) and an error probability of successfully reconstructing the secret which can be made as close to 1 as desired.
Cite as
Paolo D'Arco, Roberto De Prisco, Alfredo De Santis, Angel Pérez del Pozo, and Ugo Vaccaro. Probabilistic Secret Sharing. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{darco_et_al:LIPIcs.MFCS.2018.64,
author = {D'Arco, Paolo and De Prisco, Roberto and De Santis, Alfredo and P\'{e}rez del Pozo, Angel and Vaccaro, Ugo},
title = {{Probabilistic Secret Sharing}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {64:1--64:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.64},
URN = {urn:nbn:de:0030-drops-96464},
doi = {10.4230/LIPIcs.MFCS.2018.64},
annote = {Keywords: Secret sharing, probabilistic secret sharing, evolving secret sharing}
}
Document
Extra Space during Initialization of Succinct Data Structures and Dynamical Initializable Arrays
Abstract
Many succinct data structures on the word RAM require precomputed tables to start operating. Usually, the tables can be constructed in sublinear time. In this time, most of a data structure is not initialized, i.e., there is plenty of unused space allocated for the data structure. We present a general framework to store temporarily extra buffers between the user defined data so that the data can be processed immediately, stored first in the buffers, and then moved into the data structure after finishing the tables. As an application, we apply our framework to Dodis, Patrascu, and Thorup's data structure (STOC 2010) that emulates c-ary memory and to Farzan and Munro's succinct encoding of arbitrary graphs (TCS 2013). We also use our framework to present an in-place dynamical initializable array.
Cite as
Frank Kammer and Andrej Sajenko. Extra Space during Initialization of Succinct Data Structures and Dynamical Initializable Arrays. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 65:1-65:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{kammer_et_al:LIPIcs.MFCS.2018.65,
author = {Kammer, Frank and Sajenko, Andrej},
title = {{Extra Space during Initialization of Succinct Data Structures and Dynamical Initializable Arrays}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {65:1--65:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.65},
URN = {urn:nbn:de:0030-drops-96478},
doi = {10.4230/LIPIcs.MFCS.2018.65},
annote = {Keywords: space efficiency, succinct c-ary memory, dynamic graph representation}
}
Document
Fast Entropy-Bounded String Dictionary Look-Up with Mismatches
Abstract
We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of d strings of length m and an integer k, we must preprocess it into a data structure to answer the following queries: Given a query string Q of length m, find all strings in the dictionary that are at Hamming distance at most k from Q. Chan and Lewenstein (CPM 2015) showed a data structure for k = 1 with optimal query time O(m/w + occ), where w is the size of a machine word and occ is the size of the output. The data structure occupies O(w d log^{1+epsilon} d) extra bits of space (beyond the entropy-bounded space required to store the dictionary strings). In this work we give a solution with similar bounds for a much wider range of values k. Namely, we give a data structure that has O(m/w + log^k d + occ) query time and uses O(w d log^k d) extra bits of space.
Cite as
Pawel Gawrychowski, Gad M. Landau, and Tatiana Starikovskaya. Fast Entropy-Bounded String Dictionary Look-Up with Mismatches. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 66:1-66:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{gawrychowski_et_al:LIPIcs.MFCS.2018.66,
author = {Gawrychowski, Pawel and Landau, Gad M. and Starikovskaya, Tatiana},
title = {{Fast Entropy-Bounded String Dictionary Look-Up with Mismatches}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {66:1--66:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.66},
URN = {urn:nbn:de:0030-drops-96486},
doi = {10.4230/LIPIcs.MFCS.2018.66},
annote = {Keywords: Dictionary look-up, Hamming distance, compact data structures}
}
Document
New Results on Directed Edge Dominating Set
Abstract
We study a family of generalizations of Edge Dominating Set on directed graphs called Directed (p,q)-Edge Dominating Set. In this problem an arc (u,v) is said to dominate itself, as well as all arcs which are at distance at most q from v, or at distance at most p to u.
First, we give significantly improved FPT algorithms for the two most important cases of the problem, (0,1)-dEDS and (1,1)-dEDS (that correspond to versions of Dominating Set on line graphs), as well as polynomial kernels. We also improve the best-known approximation for these cases from logarithmic to constant. In addition, we show that (p,q)-dEDS is FPT parameterized by p+q+tw, but W-hard parameterized just by tw, where tw is the treewidth of the underlying graph of the input.
We then go on to focus on the complexity of the problem on tournaments. Here, we provide a complete classification for every possible fixed value of p,q, which shows that the problem exhibits a surprising behavior, including cases which are in P; cases which are solvable in quasi-polynomial time but not in P; and a single case (p=q=1) which is NP-hard (under randomized reductions) and cannot be solved in sub-exponential time, under standard assumptions.
Cite as
Rémy Belmonte, Tesshu Hanaka, Ioannis Katsikarelis, Eun Jung Kim, and Michael Lampis. New Results on Directed Edge Dominating Set. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 67:1-67:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{belmonte_et_al:LIPIcs.MFCS.2018.67,
author = {Belmonte, R\'{e}my and Hanaka, Tesshu and Katsikarelis, Ioannis and Kim, Eun Jung and Lampis, Michael},
title = {{New Results on Directed Edge Dominating Set}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {67:1--67:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.67},
URN = {urn:nbn:de:0030-drops-96490},
doi = {10.4230/LIPIcs.MFCS.2018.67},
annote = {Keywords: Edge Dominating Set, Tournaments, Treewidth}
}
Document
Interval-Like Graphs and Digraphs
Abstract
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all, broadly speaking, different generalizations of interval graphs, and include, in addition to interval graphs, adjusted interval digraphs, threshold graphs, complements of threshold tolerance graphs (known as `co-TT' graphs), bipartite interval containment graphs, bipartite co-circular arc graphs, and two-directional orthogonal ray graphs. (The last three classes coincide, but have been investigated in different contexts.) This common view is made possible by introducing reflexive relationships (loops) into the analysis. We also show that all the above classes are united by a common ordering characterization, the existence of a min ordering. We propose a common generalization of all these graph and digraph classes, namely signed-interval digraphs, and show that they are precisely the digraphs that are characterized by the existence of a min ordering. We also offer an alternative geometric characterization of these digraphs. For most of the above graph and digraph classes, we show that they are exactly those signed-interval digraphs that satisfy a suitable natural restriction on the digraph, like having a loop on every vertex, or having a symmetric edge-set, or being bipartite. For instance, co-TT graphs are precisely those signed-interval digraphs that have each edge symmetric. We also offer some discussion of future work on recognition algorithms and characterizations.
Cite as
Pavol Hell, Jing Huang, Ross M. McConnell, and Arash Rafiey. Interval-Like Graphs and Digraphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 68:1-68:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{hell_et_al:LIPIcs.MFCS.2018.68,
author = {Hell, Pavol and Huang, Jing and McConnell, Ross M. and Rafiey, Arash},
title = {{Interval-Like Graphs and Digraphs}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {68:1--68:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.68},
URN = {urn:nbn:de:0030-drops-96503},
doi = {10.4230/LIPIcs.MFCS.2018.68},
annote = {Keywords: graph theory, interval graphs, interval bigraphs, min ordering, co-TT graph}
}
Document
Double Threshold Digraphs
Abstract
A semiorder is a model of preference relations where each element x is associated with a utility value alpha(x), and there is a threshold t such that y is preferred to x iff alpha(y) - alpha(x) > t. These are motivated by the notion that there is some uncertainty in the utility values we assign an object or that a subject may be unable to distinguish a preference between objects whose values are close. However, they fail to model the well-known phenomenon that preferences are not always transitive. Also, if we are uncertain of the utility values, it is not logical that preference is determined absolutely by a comparison of them with an exact threshold. We propose a new model in which there are two thresholds, t_1 and t_2; if the difference alpha(y) - alpha(x) is less than t_1, then y is not preferred to x; if the difference is greater than t_2 then y is preferred to x; if it is between t_1 and t_2, then y may or may not be preferred to x. We call such a relation a (t_1,t_2) double-threshold semiorder, and the corresponding directed graph G = (V,E) a (t_1,t_2) double-threshold digraph. Every directed acyclic graph is a double-threshold digraph; increasing bounds on t_2/t_1 give a nested hierarchy of subclasses of the directed acyclic graphs. In this paper we characterize the subclasses in terms of forbidden subgraphs, and give algorithms for finding an assignment of utility values that explains the relation in terms of a given (t_1,t_2) or else produces a forbidden subgraph, and finding the minimum value lambda of t_2/t_1 that is satisfiable for a given directed acyclic graph. We show that lambda gives a useful measure of the complexity of a directed acyclic graph with respect to several optimization problems that are NP-hard on arbitrary directed acyclic graphs.
Cite as
Peter Hamburger, Ross M. McConnell, Attila Pór, Jeremy P. Spinrad, and Zhisheng Xu. Double Threshold Digraphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 69:1-69:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{hamburger_et_al:LIPIcs.MFCS.2018.69,
author = {Hamburger, Peter and McConnell, Ross M. and P\'{o}r, Attila and Spinrad, Jeremy P. and Xu, Zhisheng},
title = {{Double Threshold Digraphs}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {69:1--69:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.69},
URN = {urn:nbn:de:0030-drops-96519},
doi = {10.4230/LIPIcs.MFCS.2018.69},
annote = {Keywords: posets, preference relations, approximation algorithms}
}
Document
Tree Tribes and Lower Bounds for Switching Lemmas
Abstract
Let f be a Boolean function on n variables, rho a random p-restriction that independently keeps each variable unset (or free) with probability p and otherwise uniformly sets it to 0 or 1, and DT_{depth}(f) denote the depth of the smallest depth decision tree for f. Let R_d(f|rho) be the resilience of f to rho for depth d, defined as R_d(f|rho)=Pr_{rho < - rho}[DT_{depth}(f|rho)>= d]. If d >> pn, all functions have resilience close to 0 since less than d variables would remain unset with high probability. For d << pn, most functions f on n variables have resilience close to 1, and some functions, like AND and OR, have resilience close to 0. Håstad's Switching Lemma states that for t-DNFs, the resilience R_d(f|rho) is upper bounded by (5pt)^d, and from known upper bounds on the size of constant depth circuits computing the parity function, it follows that there exist t-DNFs whose resilience is close to the bound obtained by Håstad. However, the exact bounds for such maximally resilient DNFs or their structure is unclear, and moreover, the argument is non-constructive.
In this work, we give an explicit construction of functions called Tree Tribes parameterized by an integer t and denoted Xi_t (on n variables), such that R_d(Xi_t|rho)<=(4p2^t)^d, and more importantly, the resilience is also lower bounded by the same quantity up to constants, R_d(Xi_t|rho)>=(c_0 p2^t)^d, for 0 <= p <= c_p 2^-t and 0 <= d <= c_d * (log n)/(2^t * t log t) (where c_0,c_p,c_d are universal constants). As a result, for sufficiently large n and small d, this gives a hierarchy of functions with strictly increasing resilience, and covers the entire region between the two extremes where functions have resilience (close to) 0 or 1.
Cite as
Jenish C. Mehta. Tree Tribes and Lower Bounds for Switching Lemmas. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 70:1-70:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{mehta:LIPIcs.MFCS.2018.70,
author = {Mehta, Jenish C.},
title = {{Tree Tribes and Lower Bounds for Switching Lemmas}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {70:1--70:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.70},
URN = {urn:nbn:de:0030-drops-96524},
doi = {10.4230/LIPIcs.MFCS.2018.70},
annote = {Keywords: Tree Tribes, Resilience, Switching lemmas, lower bounds, decision tree}
}
Document
Projection Theorems Using Effective Dimension
Abstract
In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrand's projection theorem, which shows that for every analytic set E, for almost every line L, the Hausdorff dimension of the orthogonal projection of E onto L is maximal.
We use Kolmogorov complexity to give two new results on the Hausdorff and packing dimensions of orthogonal projections onto lines. The first shows that the conclusion of Marstrand's theorem holds whenever the Hausdorff and packing dimensions agree on the set E, even if E is not analytic. Our second result gives a lower bound on the packing dimension of projections of arbitrary sets. Finally, we give a new proof of Marstrand's theorem using the theory of computing.
Cite as
Neil Lutz and Donald M. Stull. Projection Theorems Using Effective Dimension. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 71:1-71:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{lutz_et_al:LIPIcs.MFCS.2018.71,
author = {Lutz, Neil and Stull, Donald M.},
title = {{Projection Theorems Using Effective Dimension}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {71:1--71:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.71},
URN = {urn:nbn:de:0030-drops-96532},
doi = {10.4230/LIPIcs.MFCS.2018.71},
annote = {Keywords: algorithmic randomness, geometric measure theory, Hausdorff dimension, Kolmogorov complexity}
}
Document
Polynomial-Time Equivalence Testing for Deterministic Fresh-Register Automata
Abstract
Register automata are one of the most studied automata models over infinite alphabets. The complexity of language equivalence for register automata is quite subtle. In general, the problem is undecidable but, in the deterministic case, it is known to be decidable and in NP. Here we propose a polynomial-time algorithm building upon automata- and group-theoretic techniques. The algorithm is applicable to standard register automata with a fixed number of registers as well as their variants with a variable number of registers and ability to generate fresh data values (fresh-register automata). To complement our findings, we also investigate the associated inclusion problem and show that it is PSPACE-complete.
Cite as
Andrzej S. Murawski, Steven J. Ramsay, and Nikos Tzevelekos. Polynomial-Time Equivalence Testing for Deterministic Fresh-Register Automata. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 72:1-72:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{murawski_et_al:LIPIcs.MFCS.2018.72,
author = {Murawski, Andrzej S. and Ramsay, Steven J. and Tzevelekos, Nikos},
title = {{Polynomial-Time Equivalence Testing for Deterministic Fresh-Register Automata}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {72:1--72:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.72},
URN = {urn:nbn:de:0030-drops-96544},
doi = {10.4230/LIPIcs.MFCS.2018.72},
annote = {Keywords: automata over infinite alphabets, language equivalence, bisimilarity, computational group theory}
}
Document
On W[1]-Hardness as Evidence for Intractability
Abstract
The central conjecture of parameterized complexity states that FPT !=W[1], and is generally regarded as the parameterized counterpart to P !=NP. We revisit the issue of the plausibility of FPT !=W[1], focusing on two aspects: the difficulty of proving the conjecture (assuming it holds), and how the relation between the two classes might differ from the one between P and NP.
Regarding the first aspect, we give new evidence that separating FPT from W[1] would be considerably harder than doing the same for P and NP. Our main result regarding the relation between FPT and W[1] states that the closure of W[1] under relativization with FPT-oracles is precisely the class W[P], implying that either FPT is not low for W[1], or the W-Hierarchy collapses. This theorem also has consequences for the A-Hierarchy (a parameterized version of the Polynomial Hierarchy), namely that unless W[P] is a subset of some level A[t], there are structural differences between the A-Hierarchy and the Polynomial Hierarchy. We also prove that under the unlikely assumption that W[P] collapses to W[1] in a specific way, the collapse of any two consecutive levels of the A-Hierarchy implies the collapse of the entire hierarchy to a finite level; this extends a result of Chen, Flum, and Grohe (2005).
Finally, we give weak (oracle-based) evidence that the inclusion W[t]subseteqA[t] is strict for t>1, and that the W-Hierarchy is proper. The latter result answers a question of Downey and Fellows (1993).
Cite as
Ralph Christian Bottesch. On W[1]-Hardness as Evidence for Intractability. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 73:1-73:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{bottesch:LIPIcs.MFCS.2018.73,
author = {Bottesch, Ralph Christian},
title = {{On W\lbrack1\rbrack-Hardness as Evidence for Intractability}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {73:1--73:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.73},
URN = {urn:nbn:de:0030-drops-96559},
doi = {10.4230/LIPIcs.MFCS.2018.73},
annote = {Keywords: Parameterized complexity, Relativization}
}
Document
A Simple Augmentation Method for Matchings with Applications to Streaming Algorithms
Abstract
Given a graph G, it is well known that any maximal matching M in G is at least half the size of a maximum matching M^*. In this paper, we show that if G is bipartite, then running the Greedy matching algorithm on a sampled subgraph of G produces enough additional edges that can be used to augment M such that the resulting matching is of size at least (2 - sqrt{2})|M^*| ~~ 0.5857 |M^*| (ignoring lower order terms) with high probability.
The main applications of our method lie in the area of data streaming algorithms, where an algorithm performs few passes over the edges of an n-vertex graph while maintaining a memory of size O(n polylog n). Our method immediately yields a very simple two-pass algorithm for Maximum Bipartite Matching (MBM) with approximation factor 0.5857, which only runs the Greedy matching algorithm in each pass. This slightly improves on the much more involved 0.583-approximation algorithm of Esfandiari et al. [ICDMW 2016]. To obtain our main result, we combine our method with a residual sparsity property of the random order Greedy algorithm and give a one-pass random order streaming algorithm for MBM with approximation factor 0.5395. This substantially improves upon the one-pass random order 0.505-approximation algorithm of Konrad et al. [APPROX 2012].
Cite as
Christian Konrad. A Simple Augmentation Method for Matchings with Applications to Streaming Algorithms. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 74:1-74:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{konrad:LIPIcs.MFCS.2018.74,
author = {Konrad, Christian},
title = {{A Simple Augmentation Method for Matchings with Applications to Streaming Algorithms}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {74:1--74:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.74},
URN = {urn:nbn:de:0030-drops-96560},
doi = {10.4230/LIPIcs.MFCS.2018.74},
annote = {Keywords: Matchings, augmenting paths, streaming algorithms, random order}
}
Document
Reconfiguration of Graph Minors
Abstract
Under the reconfiguration framework, we consider the various ways that a target graph H is a minor of a host graph G, where a subgraph of G can be transformed into H by means of edge contraction (replacement of both endpoints of an edge by a new vertex adjacent to any vertex adjacent to either endpoint). Equivalently, an H-model of G is a labeling of the vertices of G with the vertices of H, where the contraction of all edges between identically-labeled vertices results in a graph containing representations of all edges in H.
We explore the properties of G and H that result in a connected reconfiguration graph, in which nodes represent H-models and two nodes are adjacent if their corresponding H-models differ by the label of a single vertex of G. Various operations on G or H are shown to preserve connectivity. In addition, we demonstrate properties of graphs G that result in connectivity for the target graphs K_2, K_3, and K_4, including a full characterization of graphs G that result in connectivity for K_2-models, as well as the relationship between connectivity of G and other H-models.
Cite as
Benjamin Moore, Naomi Nishimura, and Vijay Subramanya. Reconfiguration of Graph Minors. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 75:1-75:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{moore_et_al:LIPIcs.MFCS.2018.75,
author = {Moore, Benjamin and Nishimura, Naomi and Subramanya, Vijay},
title = {{Reconfiguration of Graph Minors}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {75:1--75:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.75},
URN = {urn:nbn:de:0030-drops-96573},
doi = {10.4230/LIPIcs.MFCS.2018.75},
annote = {Keywords: reconfiguration, graph minors, graph algorithms}
}
Document
A Feferman-Vaught Decomposition Theorem for Weighted MSO Logic
Abstract
We prove a weighted Feferman-Vaught decomposition theorem for disjoint unions and products of finite structures. The classical Feferman-Vaught Theorem describes how the evaluation of a first order sentence in a generalized product of relational structures can be reduced to the evaluation of sentences in the contributing structures and the index structure. The logic we employ for our weighted extension is based on the weighted MSO logic introduced by Droste and Gastin to obtain a Büchi-type result for weighted automata. We show that for disjoint unions and products of structures, the evaluation of formulas from two respective fragments of the logic can be reduced to the evaluation of formulas in the contributing structures. We also prove that the respective restrictions are necessary. Surprisingly, for the case of disjoint unions, the fragment is the same as the one used in the Büchi-type result of weighted automata. In fact, even the formulas used to show that the respective restrictions are necessary are the same in both cases. However, here proving that they do not allow for a Feferman-Vaught-like decomposition is more complex and employs Ramsey's Theorem. We also show how translation schemes can be applied to go beyond disjoint unions and products.
Cite as
Manfred Droste and Erik Paul. A Feferman-Vaught Decomposition Theorem for Weighted MSO Logic. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 76:1-76:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{droste_et_al:LIPIcs.MFCS.2018.76,
author = {Droste, Manfred and Paul, Erik},
title = {{A Feferman-Vaught Decomposition Theorem for Weighted MSO Logic}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {76:1--76:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.76},
URN = {urn:nbn:de:0030-drops-96581},
doi = {10.4230/LIPIcs.MFCS.2018.76},
annote = {Keywords: Quantitative Logic, Quantitative Model Theory, Feferman-Vaught Theorem, Translation Scheme, Transduction}
}
Document
Maximum Area Axis-Aligned Square Packings
Abstract
Given a point set S={s_1,... , s_n} in the unit square U=[0,1]^2, an anchored square packing is a set of n interior-disjoint empty squares in U such that s_i is a corner of the ith square. The reach R(S) of S is the set of points that may be covered by such a packing, that is, the union of all empty squares anchored at points in S.
It is shown that area(R(S))>= 1/2 for every finite set S subset U, and this bound is the best possible. The region R(S) can be computed in O(n log n) time. Finally, we prove that finding a maximum area anchored square packing is NP-complete. This is the first hardness proof for a geometric packing problem where the size of geometric objects in the packing is unrestricted.
Cite as
Hugo A. Akitaya, Matthew D. Jones, David Stalfa, and Csaba D. Tóth. Maximum Area Axis-Aligned Square Packings. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 77:1-77:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{akitaya_et_al:LIPIcs.MFCS.2018.77,
author = {Akitaya, Hugo A. and Jones, Matthew D. and Stalfa, David and T\'{o}th, Csaba D.},
title = {{Maximum Area Axis-Aligned Square Packings}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {77:1--77:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.77},
URN = {urn:nbn:de:0030-drops-96594},
doi = {10.4230/LIPIcs.MFCS.2018.77},
annote = {Keywords: square packing, geometric optimization}
}
Document
Deterministically Counting Satisfying Assignments for Constant-Depth Circuits with Parity Gates, with Implications for Lower Bounds
Abstract
We give a deterministic algorithm for counting the number of satisfying assignments of any AC^0[oplus] circuit C of size s and depth d over n variables in time 2^(n-f(n,s,d)), where f(n,s,d) = n/O(log(s))^(d-1), whenever s = 2^o(n^(1/d)). As a consequence, we get that for each d, there is a language in E^{NP} that does not have AC^0[oplus] circuits of size 2^o(n^(1/(d+1))). This is the first lower bound in E^{NP} against AC^0[oplus] circuits that beats the lower bound of 2^Omega(n^(1/2(d-1))) due to Razborov and Smolensky for large d. Both our algorithm and our lower bounds extend to AC^0[p] circuits for any prime p.
Cite as
Ninad Rajgopal, Rahul Santhanam, and Srikanth Srinivasan. Deterministically Counting Satisfying Assignments for Constant-Depth Circuits with Parity Gates, with Implications for Lower Bounds. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 78:1-78:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{rajgopal_et_al:LIPIcs.MFCS.2018.78,
author = {Rajgopal, Ninad and Santhanam, Rahul and Srinivasan, Srikanth},
title = {{Deterministically Counting Satisfying Assignments for Constant-Depth Circuits with Parity Gates, with Implications for Lower Bounds}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {78:1--78:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.78},
URN = {urn:nbn:de:0030-drops-96607},
doi = {10.4230/LIPIcs.MFCS.2018.78},
annote = {Keywords: circuit satisfiability, circuit lower bounds, polynomial method, derandomization}
}
Document
Results on the Dimension Spectra of Planar Lines
Abstract
In this paper we investigate the (effective) dimension spectra of lines in the Euclidean plane. The dimension spectrum of a line L_{a,b}, sp(L), with slope a and intercept b is the set of all effective dimensions of the points (x, ax + b) on L. It has been recently shown that, for every a and b with effective dimension less than 1, the dimension spectrum of L_{a,b} contains an interval. Our first main theorem shows that this holds for every line. Moreover, when the effective dimension of a and b is at least 1, sp(L) contains a unit interval.
Our second main theorem gives lower bounds on the dimension spectra of lines. In particular, we show that for every alpha in [0,1], with the exception of a set of Hausdorff dimension at most alpha, the effective dimension of (x, ax + b) is at least alpha + dim(a,b)/2. As a consequence of this theorem, using a recent characterization of Hausdorff dimension using effective dimension, we give a new proof of a result by Molter and Rela on the Hausdorff dimension of Furstenberg sets.
Cite as
Donald M. Stull. Results on the Dimension Spectra of Planar Lines. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 79:1-79:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{stull:LIPIcs.MFCS.2018.79,
author = {Stull, Donald M.},
title = {{Results on the Dimension Spectra of Planar Lines}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {79:1--79:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.79},
URN = {urn:nbn:de:0030-drops-96611},
doi = {10.4230/LIPIcs.MFCS.2018.79},
annote = {Keywords: algorithmic randomness, geometric measure theory, Hausdorff dimension, Kolmogorov complexity}
}
Document
Tight Bounds for Deterministic h-Shot Broadcast in Ad-Hoc Directed Radio Networks
Abstract
We consider the classical broadcast problem in ad-hoc (that is, unknown topology) directed radio networks with no collision detection, under the additional assumption that at most h transmissions (shots) are available per node. We focus on adaptive deterministic protocols for small values of h. We provide asymptotically matching lower and upper bounds for the cases h=2 and h=3. While for h=2 our bound is quadratic, similar to the bound obtained for oblivious protocols, for h=3 we prove a sub-quadratic bound of Theta(n^2 log log n / log n), where n is the number of nodes in the network. The latter is the first result showing an adaptive algorithm which is asymptotically faster than oblivious h-shot broadcast protocols, for which a tight quadratic bound is known for every constant h. Our upper bound for h=3 is constructive, making use of constructions of graphs with large girth. We also show an improved upper bound of O(n^(1+alpha/sqrt{h})) for h >= 4, where alpha is an absolute constant independent of h. Our upper bound for h >= 4 is non-constructive.
Cite as
Aris Pagourtzis and Tomasz Radzik. Tight Bounds for Deterministic h-Shot Broadcast in Ad-Hoc Directed Radio Networks. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 80:1-80:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{pagourtzis_et_al:LIPIcs.MFCS.2018.80,
author = {Pagourtzis, Aris and Radzik, Tomasz},
title = {{Tight Bounds for Deterministic h-Shot Broadcast in Ad-Hoc Directed Radio Networks}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {80:1--80:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.80},
URN = {urn:nbn:de:0030-drops-96629},
doi = {10.4230/LIPIcs.MFCS.2018.80},
annote = {Keywords: Ad-hoc radio networks, wireless networks, deterministic broadcast, adaptive protocols, limited transmissions}
}
Document
Depth Two Majority Circuits for Majority and List Expanders
Abstract
Let MAJ_n denote the Boolean majority function of n input variables. In this paper, we study the construction of depth two circuits computing MAJ_n where each gate in a circuit computes MAJ_m for m < n.
We first give an explicit construction of depth two MAJ_{floor[n/2]+2} o MAJ_{<= n-2} circuits computing MAJ_n for every n >= 7 such that n congruent 3 (mod 4) where MAJ_m and MAJ_{<= m} denote the majority gates that take m and at most m distinct inputs, respectively. A graph theoretic argument developed by Kulikov and Podolskii (STACS '17, Article No. 49) shows that there is no MAJ_{<= n-2} o MAJ_{n-2} circuit computing MAJ_n. Hence, our construction reveals that the use of a smaller fan-in gates at the bottom level is essential for the existence of such a circuit. Some computational results are also provided.
We then show that the construction of depth two MAJ_m o MAJ_m circuits computing MAJ_n for m<n can be translated into the construction of a newly introduced version of bipartite expander graphs which we call a list expander. Intuitively, a list expander is a c-leftregular bipartite graph such that for a given d < c, every d-leftregular subgraph of the original graph has a certain expansion property. We formalize this connection and verify that, with high probability, a random bipartite graph is a list expander of certain parameters. However, the parameters obtained are not sufficient to give us a MAJ_{n-c} o MAJ_{n-c} circuit computing MAJ_n for a large constant c.
Cite as
Kazuyuki Amano. Depth Two Majority Circuits for Majority and List Expanders. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 81:1-81:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{amano:LIPIcs.MFCS.2018.81,
author = {Amano, Kazuyuki},
title = {{Depth Two Majority Circuits for Majority and List Expanders}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {81:1--81:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.81},
URN = {urn:nbn:de:0030-drops-96633},
doi = {10.4230/LIPIcs.MFCS.2018.81},
annote = {Keywords: Boolean function, majority function, constant depth circuit, expander graph}
}
Document
Optimization over the Boolean Hypercube via Sums of Nonnegative Circuit Polynomials
Abstract
Various key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems are based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS based certificates remain valid: First, there exists a SONC certificate of degree at most n+d for polynomials which are nonnegative over the n-variate boolean hypercube with constraints of degree d. Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate, that includes at most n^O(d) nonnegative circuit polynomials. Finally, we show certain differences between SOS and SONC cones: we prove that, in contrast to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar's Positivestellensatz. We discuss these results both from algebraic and optimization perspective.
Cite as
Mareike Dressler, Adam Kurpisz, and Timo de Wolff. Optimization over the Boolean Hypercube via Sums of Nonnegative Circuit Polynomials. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 82:1-82:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{dressler_et_al:LIPIcs.MFCS.2018.82,
author = {Dressler, Mareike and Kurpisz, Adam and de Wolff, Timo},
title = {{Optimization over the Boolean Hypercube via Sums of Nonnegative Circuit Polynomials}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {82:1--82:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.82},
URN = {urn:nbn:de:0030-drops-96643},
doi = {10.4230/LIPIcs.MFCS.2018.82},
annote = {Keywords: nonnegativity certificate, hypercube optimization, sums of nonnegative circuit polynomials, relative entropy programming, sums of squares}
}
Document
Rainbow Vertex Coloring Bipartite Graphs and Chordal Graphs
Abstract
Given a graph with colors on its vertices, a path is called a rainbow vertex path if all its internal vertices have distinct colors. We say that the graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. We study the problem of deciding whether the vertices of a given graph can be colored with at most k colors so that the graph becomes rainbow vertex-connected. Although edge-colorings have been studied extensively under similar constraints, there are significantly fewer results on the vertex variant that we consider. In particular, its complexity on structured graph classes was explicitly posed as an open question.
We show that the problem remains NP-complete even on bipartite apex graphs and on split graphs. The former can be seen as a first step in the direction of studying the complexity of rainbow coloring on sparse graphs, an open problem which has attracted attention but limited progress. We also give hardness of approximation results for both bipartite and split graphs. To complement the negative results, we show that bipartite permutation graphs, interval graphs, and block graphs can be rainbow vertex-connected optimally in polynomial time.
Cite as
Pinar Heggernes, Davis Issac, Juho Lauri, Paloma T. Lima, and Erik Jan van Leeuwen. Rainbow Vertex Coloring Bipartite Graphs and Chordal Graphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 83:1-83:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{heggernes_et_al:LIPIcs.MFCS.2018.83,
author = {Heggernes, Pinar and Issac, Davis and Lauri, Juho and Lima, Paloma T. and van Leeuwen, Erik Jan},
title = {{Rainbow Vertex Coloring Bipartite Graphs and Chordal Graphs}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {83:1--83:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.83},
URN = {urn:nbn:de:0030-drops-96657},
doi = {10.4230/LIPIcs.MFCS.2018.83},
annote = {Keywords: Rainbow coloring, graph classes, polynomial-time algorithms, approximation algorithms}
}
Document
Listing Subgraphs by Cartesian Decomposition
Abstract
We investigate a decomposition technique for listing problems in graphs and set systems. It is based on the Cartesian product of some iterators, which list the solutions of simpler problems. Our ideas applies to several problems, and we illustrate one of them in depth, namely, listing all minimum spanning trees of a weighted graph G. Here iterators over the spanning trees for unweighted graphs can be obtained by a suitable modification of the listing algorithm by [Shioura et al., SICOMP 1997], and the decomposition of G is obtained by suitably partitioning its edges according to their weights. By combining these iterators in a Cartesian product scheme that employs Gray coding, we give the first algorithm which lists all minimum spanning trees of G in constant delay, where the delay is the time elapsed between any two consecutive outputs. Our solution requires polynomial preprocessing time and uses polynomial space.
Cite as
Alessio Conte, Roberto Grossi, Andrea Marino, Romeo Rizzi, and Luca Versari. Listing Subgraphs by Cartesian Decomposition. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 84:1-84:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
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@InProceedings{conte_et_al:LIPIcs.MFCS.2018.84,
author = {Conte, Alessio and Grossi, Roberto and Marino, Andrea and Rizzi, Romeo and Versari, Luca},
title = {{Listing Subgraphs by Cartesian Decomposition}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {84:1--84:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Potapov, Igor and Spirakis, Paul and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.84},
URN = {urn:nbn:de:0030-drops-96666},
doi = {10.4230/LIPIcs.MFCS.2018.84},
annote = {Keywords: Graph algorithms, listing, minimum spanning trees, constant delay}
}