Volume
LIPIcs, Volume 30
32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
Event
STACS 2015, March 4-7, 2015, Garching, GermanyEditors
Publication Details
- published at: 2015-02-26
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-939897-78-1
- DBLP: db/conf/stacs/stacs2015
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Document
Complete Volume
LIPIcs, Volume 30, STACS'15, Complete Volume
Abstract
LIPIcs, Volume 30, STACS'15, Complete Volume
Cite as
32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@Proceedings{mayr_et_al:LIPIcs.STACS.2015,
title = {{LIPIcs, Volume 30, STACS'15, Complete Volume}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015},
URN = {urn:nbn:de:0030-drops-49630},
doi = {10.4230/LIPIcs.STACS.2015},
annote = {Keywords: Models of Computation, Nonnumerical Algorithms and Problems, Mathematical Logic, Formal Languages, Combinatorics, Graph Theory}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. i-xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{mayr_et_al:LIPIcs.STACS.2015.i,
author = {Mayr, Ernst W. and Ollinger, Nicolas},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {i--xviii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.i},
URN = {urn:nbn:de:0030-drops-49615},
doi = {10.4230/LIPIcs.STACS.2015.i},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
Overcoming Intractability in Unsupervised Learning (Invited Talk)
Abstract
Unsupervised learning - i.e., learning with unlabeled data - is increasingly important given today's data deluge. Most natural problems in this domain - e.g. for models such as mixture models, HMMs, graphical models, topic models and sparse coding/dictionary learning, deep learning - are NP-hard. Therefore researchers in practice use either heuristics or convex relaxations with no concrete approximation bounds. Several nonconvex heuristics work well in practice, which is also a mystery.
The talk will describe a sequence of recent results whereby rigorous approaches leading to polynomial running time are possible for several problems in unsupervised learning. The proof of polynomial running time usually relies upon nondegeneracy assumptions on the data and the model parameters, and often also on stochastic properties of the data (average-case analysis). We describe results for topic models, sparse coding, and deep learning. Some of these new algorithms are very efficient and practical - e.g. for topic modeling.
Cite as
Sanjeev Arora. Overcoming Intractability in Unsupervised Learning (Invited Talk). In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, p. 1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{arora:LIPIcs.STACS.2015.1,
author = {Arora, Sanjeev},
title = {{Overcoming Intractability in Unsupervised Learning}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {1--1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.1},
URN = {urn:nbn:de:0030-drops-49581},
doi = {10.4230/LIPIcs.STACS.2015.1},
annote = {Keywords: machine learning, unsupervised learning, intractability, NP-hardness}
}
Document
Invited Talk
The Complexity of Constraint Satisfaction Problems (Invited Talk)
Abstract
The tractability conjecture for constraint satisfaction problems (CSPs)
describes the constraint languages over a finite domain whose CSP can be solved in polynomial-time. The precise formulation of the conjecture
uses basic notions from universal algebra. In this talk, we give a short introduction to the universal-algebraic approach to the study of the complexity of CSPs. Finally, we discuss attempts to generalise the tractability conjecture to large classes of constraint languages over infinite domains, in particular for constraint languages that arise in qualitative temporal and spatial reasoning.
Cite as
Manuel Bodirsky. The Complexity of Constraint Satisfaction Problems (Invited Talk). In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 2-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{bodirsky:LIPIcs.STACS.2015.2,
author = {Bodirsky, Manuel},
title = {{The Complexity of Constraint Satisfaction Problems}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {2--9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.2},
URN = {urn:nbn:de:0030-drops-49567},
doi = {10.4230/LIPIcs.STACS.2015.2},
annote = {Keywords: constraint satisfaction, universal algebra, model theory, clones, temporal and spatial reasoning}
}
Document
Invited Talk
Parallel Algorithms Reconsidered (Invited Talk)
Abstract
Parallel algorithms have been a subject of intensive algorithmic research in the 1980s. This research almost died out in the mid 1990s. In this paper we argue that it is high time to reconsider this subject since a lot of things have changed. First and foremost, parallel processing has moved from a niche application to something mandatory for any performance critical computer applications. We will also point out that even very fundamental results can still be obtained. We give examples and also formulate some open problems.
Cite as
Peter Sanders. Parallel Algorithms Reconsidered (Invited Talk). In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 10-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{sanders:LIPIcs.STACS.2015.10,
author = {Sanders, Peter},
title = {{Parallel Algorithms Reconsidered}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {10--18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.10},
URN = {urn:nbn:de:0030-drops-49572},
doi = {10.4230/LIPIcs.STACS.2015.10},
annote = {Keywords: parallel algorithm, algorithm engineering, communication efficient algorithm, polylogarithmic time algorithm, parallel machine model}
}
Document
Tutorial
Computational Social Choice (Tutorial)
Abstract
Over the past few years there has been a lively exchange of ideas between computer science, in particular theoretical computer science and artificial intelligence, on the one hand and economics, in particular game theory and social choice, on the other. This exchange goes in both directions and has produced active research areas such as algorithmic game theory and computational social choice.
Social choice theory concerns the formal analysis and design of methods for aggregating possibly conflicting preferences such as in voting, assignment, or matching problems. Much of the work in classic social choice theory has focused on results concerning the formal possibility and impossibility of aggregation functions that combine desirable properties.
This tutorial provided an overview of central results in social choice theory with a special focus on axiomatic characterizations as well as computational aspects. While some aggregation functions can be easily computed, others have been shown to be computationally intractable (e.g., NP-hard or #P-hard). Topics that were covered in this tutorial included (i) rational choice theory, (ii) Arrow's impossibility theorem, (iii) tournament solutions (such as the top cycle, the uncovered set, the Banks set, or the tournament equilibrium set), and (iv) randomized social choice functions. The overarching theme were escape routes from negative results such as Arrow's impossibility theorem.
Cite as
Felix Brandt. Computational Social Choice (Tutorial). In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, p. 19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{brandt:LIPIcs.STACS.2015.19,
author = {Brandt, Felix},
title = {{Computational Social Choice}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {19--19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.19},
URN = {urn:nbn:de:0030-drops-49593},
doi = {10.4230/LIPIcs.STACS.2015.19},
annote = {Keywords: social choice theory, economics, algorithms, theory}
}
Document
Tutorial
Algorithmic Game Theory (Tutorial)
Abstract
Game theory studies mathematical models of interactions amongst self-interested entities. A "solution concept" means a description of the outcome of a game, and it is important that it should be defined in such a way that a solution always exists (every game should have an outcome). Nash's famous theorem that mixed-strategy equilibria are guaranteed to exist, resulted in Nash equilibrium being the most prominent solution concept in game theory.
As a result, computational challenges of the form "given a game, find a solution", have the property that we are searching for something whose existence is guaranteed (they are total search problems). Moreover, these solutions belong to the complexity class NP, since it is usually straightforward to check whether a proposed solution is correct (an incorrect one will admit a profitable deviation by one or more of the players, and this is usually easy to find). However, in versions of the problem that appear to be computationally hard, we cannot apply NP-completeness, due to a result of Megiddo saying that total search problems cannot be NP-complete unless NP is equal to co-NP.
In this tutorial, which is intended for people familiar with NP-completeness, I give an overview of the alternative notions of computational hardness that apply to game-theoretic solution concepts. I discuss the complexity class PPAD (introduced by Papadimitriou) which captures the computational complexity of various classes of games that don’t seem to be solvable in polynomial time. I also mention the complexity classes PLS and FIXP, and the kinds of games that they apply to.
Suppose, alternatively, that we have a polynomial-time algorithm that applies to some given class of games. A follow-up question is whether there exist algorithms that find a solution via processes that reflect decentralised selfish behaviour. This is because a solution concept arguably remains unrealistic if it can be efficiently computed, but only using a highly centralised algorithm. In the second half of the tutorial I present some results on learning dynamics for equilibrium computation, and mention recent work on communication complexity and query complexity.
I discuss some research directions and open problems, such as the following. What are the prospects for proving that PPAD is as hard as NP? How about algorithms that find improved approximate Nash equilibria? 2-player games are easy to solve in practice, using the Lemke-Howson algorithm, so is there a satisfying mathematical sense in which 2-player games are easy to solve? (For example, a sense in which Lemke-Howson works "most of the time"?)
Cite as
Paul W. Goldberg. Algorithmic Game Theory (Tutorial). In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, p. 20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{goldberg:LIPIcs.STACS.2015.20,
author = {Goldberg, Paul W.},
title = {{Algorithmic Game Theory}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {20--20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.20},
URN = {urn:nbn:de:0030-drops-49606},
doi = {10.4230/LIPIcs.STACS.2015.20},
annote = {Keywords: equilibrium, non-cooperative games, computational complexity}
}
Document
The Minimum Oracle Circuit Size Problem
Abstract
We consider variants of the Minimum Circuit Size Problem MCSP, where the goal is to minimize the size of oracle circuits computing a given function. When the oracle is QBF, the resulting problem MCSP^QBF
is known to be complete for PSPACE under ZPP reductions. We show that it is not complete under logspace reductions, and indeed it is not even hard for TC under uniform AC^0 reductions. We obtain a variety of consequences that follow if oracle versions of MCSP are hard for various complexity classes under different types of reductions. We also prove analogous results for the problem of determining the resource-bounded Kolmogorov complexity of strings, for certain types of Kolmogorov complexity measures.
Cite as
Eric Allender, Dhiraj Holden, and Valentine Kabanets. The Minimum Oracle Circuit Size Problem. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 21-33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{allender_et_al:LIPIcs.STACS.2015.21,
author = {Allender, Eric and Holden, Dhiraj and Kabanets, Valentine},
title = {{The Minimum Oracle Circuit Size Problem}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {21--33},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.21},
URN = {urn:nbn:de:0030-drops-49013},
doi = {10.4230/LIPIcs.STACS.2015.21},
annote = {Keywords: Kolmogorov complexity, minimum circuit size problem, PSPACE, NP-intermediate sets}
}
Document
Graph Searching Games and Width Measures for Directed Graphs
Abstract
In cops and robber games a number of cops tries to capture a robber in
a graph. A variant of these games on undirected graphs characterises tree width by the least number of cops needed to win. We consider cops and robber games on digraphs and width measures (such as DAG-width, directed tree width or D-width) corresponding to them. All of them generalise tree width and the game characterising it.
For the DAG-width game we prove that the problem to decide the minimal
number of cops required to capture the robber (which is the same as deciding DAG-width), is PSPACE-complete, in contrast to most other similar games. We also show that the cop-monotonicity cost for directed tree width games cannot be bounded by any function. As a consequence, D-width is not bounded in directed tree width, refuting a conjecture by Safari.
A large number of directed width measures generalising tree width has been proposed in the literature. However, only very little was known about the relation between them, in particular about whether classes of digraphs of bounded width in one measure have bounded width in another. In this paper we establish an almost complete order among the most prominent width measures with respect to mutual boundedness.
Cite as
Saeed Akhoondian Amiri, Lukasz Kaiser, Stephan Kreutzer, Roman Rabinovich, and Sebastian Siebertz. Graph Searching Games and Width Measures for Directed Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 34-47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{akhoondianamiri_et_al:LIPIcs.STACS.2015.34,
author = {Akhoondian Amiri, Saeed and Kaiser, Lukasz and Kreutzer, Stephan and Rabinovich, Roman and Siebertz, Sebastian},
title = {{Graph Searching Games and Width Measures for Directed Graphs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {34--47},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.34},
URN = {urn:nbn:de:0030-drops-49020},
doi = {10.4230/LIPIcs.STACS.2015.34},
annote = {Keywords: cops and robber games, directed graphs, DAG-width}
}
Document
Subset Sum in the Absence of Concentration
Abstract
We study the exact time complexity of the Subset Sum problem. Our focus is on instances that lack additive structure in the sense that the sums one can form from the subsets of the given integers are not strongly concentrated on any particular integer value. We present a randomized algorithm that runs in O(2^0.3399nB^4) time on instances with the property that no value can arise as a sum of more than B different subsets of the n given integers.
Cite as
Per Austrin, Petteri Kaski, Mikko Koivisto, and Jesper Nederlof. Subset Sum in the Absence of Concentration. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 48-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{austrin_et_al:LIPIcs.STACS.2015.48,
author = {Austrin, Per and Kaski, Petteri and Koivisto, Mikko and Nederlof, Jesper},
title = {{Subset Sum in the Absence of Concentration}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {48--61},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.48},
URN = {urn:nbn:de:0030-drops-49034},
doi = {10.4230/LIPIcs.STACS.2015.48},
annote = {Keywords: subset sum, additive combinatorics, exponential-time algorithm, homomorphic hashing, Littlewood--Offord problem}
}
Document
On Sharing, Memoization, and Polynomial Time
Abstract
We study how the adoption of an evaluation mechanism with sharing and memoization impacts the class of functions which can be computed in polynomial time. We first show how a natural cost model in which lookup for an already computed result has no cost is indeed invariant. As a corollary, we then prove that the most general notion of ramified recurrence is sound for polynomial time, this way settling an open problem in implicit computational complexity.
Cite as
Martin Avanzini and Ugo Dal Lago. On Sharing, Memoization, and Polynomial Time. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 62-75, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{avanzini_et_al:LIPIcs.STACS.2015.62,
author = {Avanzini, Martin and Dal Lago, Ugo},
title = {{On Sharing, Memoization, and Polynomial Time}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {62--75},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.62},
URN = {urn:nbn:de:0030-drops-49042},
doi = {10.4230/LIPIcs.STACS.2015.62},
annote = {Keywords: implicit computational complexity, data-tiering, polynomial time}
}
Document
Proof Complexity of Resolution-based QBF Calculi
Abstract
Proof systems for quantified Boolean formulas (QBFs) provide a theoretical underpinning for the performance of important QBF solvers.
However, the proof complexity of these proof systems is currently not well understood and in particular lower bound techniques are missing.
In this paper we exhibit a new and elegant proof technique for showing lower bounds in QBF proof systems based on strategy extraction. This technique provides a direct transfer of circuit lower bounds to lengths of proofs lower bounds. We use our method to show the hardness of a natural class of parity formulas for Q-resolution and universal Q-resolution. Variants of the formulas are hard for even stronger systems as long-distance Q-resolution and extensions. With a completely different lower bound argument we show the hardness of the prominent formulas of Kleine Büning et al. [34] for the strong expansion-based calculus IR-calc. Our lower bounds imply new exponential separations between two different types of resolution-based QBF calculi: proof systems for CDCL-based solvers (Q-resolution, long-distance Q-resolution) and proof systems for expansion-based solvers (forallExp+Res and its generalizations IR-calc and IRM-calc). The relations between proof systems from the two different classes were not known before.
Cite as
Olaf Beyersdorff, Leroy Chew, and Mikolás Janota. Proof Complexity of Resolution-based QBF Calculi. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 76-89, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{beyersdorff_et_al:LIPIcs.STACS.2015.76,
author = {Beyersdorff, Olaf and Chew, Leroy and Janota, Mikol\'{a}s},
title = {{Proof Complexity of Resolution-based QBF Calculi}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {76--89},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.76},
URN = {urn:nbn:de:0030-drops-49057},
doi = {10.4230/LIPIcs.STACS.2015.76},
annote = {Keywords: proof complexity, QBF, lower bound techniques, separations}
}
Document
Welfare Maximization with Friends-of-Friends Network Externalities
Abstract
Online social networks allow the collection of large amounts of data about the influence between users connected by a friendship-like relationship. When distributing items among agents forming a social network, this information allows us to exploit network externalities that each agent receives from his neighbors that get the same item. In this paper we consider Friends-of-Friends (2-hop) network externalities, i.e., externalities that not only depend on the neighbors that get the same item but also on neighbors of neighbors. For these externalities we study a setting where multiple different items are assigned to unit-demand agents. Specifically, we study the problem of welfare maximization under different types of externality functions. Let n be the number of agents and m be the number of items. Our contributions are the following: (1) We show that welfare maximization is APX-hard; we show that even for step functions with 2-hop (and also with 1-hop) externalities it is NP-hard to approximate social welfare better than (1-1/e). (2) On the positive side we present (i) an O(sqrt n)-approximation algorithm for general concave externality functions,
(ii) an O(\log m)-approximation algorithm for linear externality functions, and (iii) an (1-1/e)\frac{1}{6}-approximation algorithm for 2-hop step function externalities. We also improve the result from [6] for 1-hop step function externalities by giving a (1-1/e)/2-approximation algorithm.
Cite as
Sayan Bhattacharya, Wolfgang Dvorák, Monika Henzinger, and Martin Starnberger. Welfare Maximization with Friends-of-Friends Network Externalities. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 90-102, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{bhattacharya_et_al:LIPIcs.STACS.2015.90,
author = {Bhattacharya, Sayan and Dvor\'{a}k, Wolfgang and Henzinger, Monika and Starnberger, Martin},
title = {{Welfare Maximization with Friends-of-Friends Network Externalities}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {90--102},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.90},
URN = {urn:nbn:de:0030-drops-49066},
doi = {10.4230/LIPIcs.STACS.2015.90},
annote = {Keywords: network externalities, welfare maximization, approximation algorithms}
}
Document
Markov Decision Processes and Stochastic Games with Total Effective Payoff
Abstract
We consider finite Markov decision processes (MDPs) with undiscounted total effective payoff. We show that there exist uniformly optimal pure stationary strategies that can be computed by solving a polynomial
number of linear programs. We apply this result to two-player zero-sum stochastic games with perfect information and undiscounted total effective payoff, and derive the existence of a saddle point in uniformly optimal pure stationary strategies.
Cite as
Endre Boros, Khaled Elbassioni, Vladimir Gurvich, and Kazuhisa Makino. Markov Decision Processes and Stochastic Games with Total Effective Payoff. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 103-115, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{boros_et_al:LIPIcs.STACS.2015.103,
author = {Boros, Endre and Elbassioni, Khaled and Gurvich, Vladimir and Makino, Kazuhisa},
title = {{Markov Decision Processes and Stochastic Games with Total Effective Payoff}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {103--115},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.103},
URN = {urn:nbn:de:0030-drops-49074},
doi = {10.4230/LIPIcs.STACS.2015.103},
annote = {Keywords: Markov decision processes, undiscounted stochastic games, linear programming, mean payoff, total payoff}
}
Document
Advice Complexity for a Class of Online Problems
Abstract
The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. We determine the advice complexity of a number of hard online problems including independent set, vertex cover, dominating set and several others. These problems are hard, since a single wrong answer by the online algorithm can have devastating consequences. For each of these problems, we show that \log\left(1+\frac{(c-1)^{c-1}}{c^{c}}\right)n=\Theta (n/c) bits of advice are necessary and sufficient (up to an additive term of O(\log n)) to achieve a competitive ratio of c. This is done by introducing a new string guessing problem related to those of Emek et al. (TCS 2011) and Böckenhauer et al. (TCS 2014). It turns out that this gives a powerful but easy-to-use method for providing both upper and lower bounds on the advice complexity of an entire class of online problems.
Previous results of Halldórsson et al. (TCS 2002) on online independent set, in a related model, imply that the advice complexity of the problem is \Theta (n/c). Our results improve on this by providing an exact formula for the higher-order term. Böckenhauer et al. (ISAAC 2009) gave a lower bound of \Omega (n/c) and an upper bound of O((n\log c)/c) on the advice complexity of online disjoint path allocation. We improve on the upper bound by a factor of $\log c$. For the remaining problems, no bounds on their advice complexity were previously known.
Cite as
Joan Boyar, Lene M. Favrholdt, Christian Kudahl, and Jesper W. Mikkelsen. Advice Complexity for a Class of Online Problems. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 116-129, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{boyar_et_al:LIPIcs.STACS.2015.116,
author = {Boyar, Joan and Favrholdt, Lene M. and Kudahl, Christian and Mikkelsen, Jesper W.},
title = {{Advice Complexity for a Class of Online Problems}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {116--129},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.116},
URN = {urn:nbn:de:0030-drops-49086},
doi = {10.4230/LIPIcs.STACS.2015.116},
annote = {Keywords: online algorithms, advice complexity, asymmetric string guessing, advice complexity class AOC, covering designs}
}
Document
Las Vegas Computability and Algorithmic Randomness
Abstract
In this article we try to formalize the question "What can be computed with access to randomness?" We propose the very fine-grained Weihrauch lattice as an approach to differentiate between different types of computation with access to randomness. In particular, we show that a natural concept of Las Vegas computability on infinite objects is more powerful than mere oracle access to a Martin-Löf random object. As a concrete problem that is Las Vegas computable but not computable with access to a Martin-Löf random oracle we study the problem of finding Nash equilibria.
Cite as
Vasco Brattka, Guido Gherardi, and Rupert Hölzl. Las Vegas Computability and Algorithmic Randomness. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 130-142, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{brattka_et_al:LIPIcs.STACS.2015.130,
author = {Brattka, Vasco and Gherardi, Guido and H\"{o}lzl, Rupert},
title = {{Las Vegas Computability and Algorithmic Randomness}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {130--142},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.130},
URN = {urn:nbn:de:0030-drops-49093},
doi = {10.4230/LIPIcs.STACS.2015.130},
annote = {Keywords: Weihrauch degrees, weak weak K\"{o}nig's lemma, Las Vegas computability, algorithmic randomness, Nash equilibria}
}
Document
Understanding Model Counting for beta-acyclic CNF-formulas
Abstract
We show that SAT on beta-acyclic CNF-formulas can be solved in polynomial time. In contrast to previous algorithms for other structurally restricted classes of formulas, our algorithm does not proceed by dynamic programming. Instead, it works along an elimination order, solving a weighted version of constraint satisfaction. We give evidence that this deviation from more standard algorithms is no coincidence by showing that it is outside of the framework recently proposed by Saether et al. (SAT 2014) which subsumes all other structural tractability results for #SAT known so far.
Cite as
Johann Brault-Baron, Florent Capelli, and Stefan Mengel. Understanding Model Counting for beta-acyclic CNF-formulas. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 143-156, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{braultbaron_et_al:LIPIcs.STACS.2015.143,
author = {Brault-Baron, Johann and Capelli, Florent and Mengel, Stefan},
title = {{Understanding Model Counting for beta-acyclic CNF-formulas}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {143--156},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.143},
URN = {urn:nbn:de:0030-drops-49106},
doi = {10.4230/LIPIcs.STACS.2015.143},
annote = {Keywords: model counting, hypergraph acyclicity, structural tractability}
}
Document
Parameterized Complexity Dichotomy for Steiner Multicut
Abstract
We consider the Steiner Multicut problem, which asks, given an undirected graph G, a collection T = \{T_{1},...,T_{t}}, T_i \subseteq V(G), of terminal sets of size at most p, and an integer k, whether there is a set S of at most k edges or nodes such that of each set T_{i} at least one pair of terminals is in different connected components of G \ S. This problem generalizes several well-studied graph cut problems, in particular the Multicut problem, which corresponds to the case p = 2. The Multicut problem was recently shown to be fixed-parameter tractable for parameter k [Marx and Razgon, Bousquet et al., STOC 2011]. The question whether this result generalizes to Steiner Multicut motivates the present work.
We answer the question that motivated this work, and in fact provide a dichotomy of the parameterized complexity of Steiner Multicut on general graphs. That is, for any combination of k, t, p, and the treewidth tw(G) as constant, parameter, or unbounded, and for all versions of the problem (edge deletion and node deletion with and without deletable terminals), we prove either that the problem is fixed-parameter tractable or that the problem is hard (W[1]-hard or even (para-)NP-complete). Among the many results in the paper, we highlight that:
- The edge deletion version of Steiner Multicut is fixed-parameter tractable for parameter k+t on general graphs (but has no polynomial kernel, even on trees).
- In contrast, both node deletion versions of Steiner Multicut are W[1]-hard for the parameter k+t on general graphs.
- All versions of Steiner Multicut are W[1]-hard for the parameter k, even when p=3 and the graph is a tree plus one node.
Since we allow k, t, p, and tw(G) to be any constants, our characterization includes a dichotomy for Steiner Multicut on trees (for tw(G) = 1) as well as a polynomial time versus NP-hardness dichotomy (by restricting k,t,p,tw(G) to constant or unbounded).
Cite as
Karl Bringmann, Danny Hermelin, Matthias Mnich, and Erik Jan van Leeuwen. Parameterized Complexity Dichotomy for Steiner Multicut. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 157-170, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{bringmann_et_al:LIPIcs.STACS.2015.157,
author = {Bringmann, Karl and Hermelin, Danny and Mnich, Matthias and van Leeuwen, Erik Jan},
title = {{Parameterized Complexity Dichotomy for Steiner Multicut}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {157--170},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.157},
URN = {urn:nbn:de:0030-drops-49115},
doi = {10.4230/LIPIcs.STACS.2015.157},
annote = {Keywords: graph cut problems, Steiner cut, fixed-parameter tractability}
}
Document
Solving Totally Unimodular LPs with the Shadow Vertex Algorithm
Abstract
We show that the shadow vertex simplex algorithm can be used to solve linear programs in strongly polynomial time with respect to the number n of variables, the number m of constraints, and 1/\delta, where \delta is a parameter that measures the flatness of the vertices of the polyhedron. This extends our recent result that the shadow vertex algorithm finds paths of polynomial length (w.r.t. n, m, and 1/delta) between two given vertices of a polyhedron [4].
Our result also complements a recent result due to Eisenbrand and Vempala [6] who have shown that a certain version of the random edge pivot rule solves linear programs with a running time that is strongly polynomial in the number of variables n and 1/\delta, but independent of the number m of constraints. Even though the running time of our algorithm depends on m, it is significantly faster for the important special case of totally unimodular linear programs, for which 1/delta\le n and which have only O(n^2) constraints.
Cite as
Tobias Brunsch, Anna Großwendt, and Heiko Röglin. Solving Totally Unimodular LPs with the Shadow Vertex Algorithm. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 171-183, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{brunsch_et_al:LIPIcs.STACS.2015.171,
author = {Brunsch, Tobias and Gro{\ss}wendt, Anna and R\"{o}glin, Heiko},
title = {{Solving Totally Unimodular LPs with the Shadow Vertex Algorithm}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {171--183},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.171},
URN = {urn:nbn:de:0030-drops-49125},
doi = {10.4230/LIPIcs.STACS.2015.171},
annote = {Keywords: linear optimization, simplex algorithm, shadow vertex method}
}
Document
Improved Local Search for Geometric Hitting Set
Abstract
Over the past several decades there has been steady progress towards the goal of polynomial-time approximation schemes (PTAS) for fundamental geometric combinatorial optimization problems. A foremost example is the geometric hitting set problem: given a set P of points and a set D of geometric objects, compute the minimum-sized subset of P that hits all objects in D. For the case where D is a set of disks in the plane, a PTAS was finally achieved in 2010, with a surprisingly simple algorithm based on local-search. Since then, local-search has turned out to be a powerful algorithmic approach towards achieving good approximation ratios for geometric problems (for geometric independent-set problem, for dominating sets, for the terrain guarding problem and several others).
Unfortunately all these algorithms have the same limitation: local search is able to give a PTAS, but with large running times. That leaves open the question of whether a better understanding - both combinatorial and algorithmic - of local search and the problem can give a better approximation ratio in a more reasonable time. In this paper, we investigate this question for hitting sets for disks in the plane. We present tight approximation bounds for (3,2)-local search and give an (8+\epsilon)-approximation algorithm with expected running time ˜O(n^{2.34}); the previous-best result achieving a similar approximation ratio gave a 10-approximation in time O(n^{15}) -- that too just for unit disks. The techniques and ideas generalize to (4,3) local search. Furthermore, as mentioned earlier, local-search has been used for several other geometric optimization problems; for all these problems our results show that (3,2) local search gives an 8-approximation and no better \footnote{This is assuming the use of the standard framework. Improvement of the approximation factor by using additional properties specific to the problem may be possible.}. Similarly (4,3)-local search gives a 5-approximation for all these problems.
Cite as
Norbert Bus, Shashwat Garg, Nabil H. Mustafa, and Saurabh Ray. Improved Local Search for Geometric Hitting Set. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 184-196, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{bus_et_al:LIPIcs.STACS.2015.184,
author = {Bus, Norbert and Garg, Shashwat and Mustafa, Nabil H. and Ray, Saurabh},
title = {{Improved Local Search for Geometric Hitting Set}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {184--196},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.184},
URN = {urn:nbn:de:0030-drops-49135},
doi = {10.4230/LIPIcs.STACS.2015.184},
annote = {Keywords: hitting sets, Delaunay triangulation, local search, disks, geometric algorithms}
}
Document
Arc Diagrams, Flip Distances, and Hamiltonian Triangulations
Abstract
We show that every triangulation (maximal planar graph) on n\ge 6 vertices can be flipped into a Hamiltonian triangulation using a sequence of less than n/2 combinatorial edge flips. The previously best upper bound uses 4-connectivity as a means to establish Hamiltonicity. But in general about 3n/5 flips are necessary to reach a 4-connected triangulation. Our result improves the upper bound on the diameter of the flip graph of combinatorial triangulations on n vertices from 5.2n-33.6 to 5n-23. We also show that for every triangulation on n vertices there is a simultaneous flip of less than 2n/3 edges to a 4-connected triangulation. The bound on the number of edges is tight, up to an additive constant. As another application we show that every planar graph on n vertices admits an arc diagram with less than n/2 biarcs, that is, after subdividing less than n/2 (of potentially 3n-6) edges the resulting graph admits a 2-page book embedding.
Cite as
Jean Cardinal, Michael Hoffmann, Vincent Kusters, Csaba D. Tóth, and Manuel Wettstein. Arc Diagrams, Flip Distances, and Hamiltonian Triangulations. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 197-210, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{cardinal_et_al:LIPIcs.STACS.2015.197,
author = {Cardinal, Jean and Hoffmann, Michael and Kusters, Vincent and T\'{o}th, Csaba D. and Wettstein, Manuel},
title = {{Arc Diagrams, Flip Distances, and Hamiltonian Triangulations}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {197--210},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.197},
URN = {urn:nbn:de:0030-drops-49141},
doi = {10.4230/LIPIcs.STACS.2015.197},
annote = {Keywords: graph embeddings, edge flips, flip graph, separating triangles}
}
Document
Tractable Probabilistic mu-Calculus That Expresses Probabilistic Temporal Logics
Abstract
We revisit a recently introduced probabilistic \mu-calculus and study an expressive fragment of it. By using the probabilistic quantification as an atomic operation of the calculus we establish a connection between the calculus and obligation games. The calculus we consider is strong enough to encode well-known logics such as pctl and pctl^*. Its game semantics is very similar to the game semantics of the classical mu-calculus (using parity obligation games instead of parity games).
This leads to an optimal complexity of NP\cap co-NP for its finite model checking procedure. Furthermore, we investigate a (relatively) well-behaved fragment of this calculus: an extension of pctl with fixed points. An important feature of this extended version of pctl is that its model checking is only exponential w.r.t. the alternation depth of
fixed points, one of the main characteristics of Kozen's mu-calculus.
Cite as
Pablo Castro, Cecilia Kilmurray, and Nir Piterman. Tractable Probabilistic mu-Calculus That Expresses Probabilistic Temporal Logics. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 211-223, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{castro_et_al:LIPIcs.STACS.2015.211,
author = {Castro, Pablo and Kilmurray, Cecilia and Piterman, Nir},
title = {{Tractable Probabilistic mu-Calculus That Expresses Probabilistic Temporal Logics}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {211--223},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.211},
URN = {urn:nbn:de:0030-drops-49155},
doi = {10.4230/LIPIcs.STACS.2015.211},
annote = {Keywords: mu-calculus, probabilistic logics, model checking, game semantics}
}
Document
Tribes Is Hard in the Message Passing Model
Abstract
We consider the point-to-point message passing model of communication in which there are $k$ processors with individual private inputs, each n-bit long. Each processor is located at the node of an underlying undirected graph and has access to private random coins. An edge of the graph is a private channel of communication between its endpoints. The processors have to compute a given function of all their inputs by communicating along these channels. While this model has been widely used in distributed computing, strong lower bounds on the amount of communication needed to compute simple functions have just begun to appear.
In this work, we prove a tight lower bound of \Omega(kn) on the communication needed for computing the Tribes function, when the underlying graph is a star of k+1 nodes that has k leaves with inputs and a center with no input. A lower bound on this topology easily implies comparable bounds for others. Our lower bounds are obtained by building upon the recent information theoretic techniques of Braverman et al. ([4], FOCS'13) and combining it with the earlier work of Jayram, Kumar and Sivakumar ([10], STOC'03). This approach yields information complexity bounds that are of independent interest.
Cite as
Arkadev Chattopadhyay and Sagnik Mukhopadhyay. Tribes Is Hard in the Message Passing Model. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 224-237, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{chattopadhyay_et_al:LIPIcs.STACS.2015.224,
author = {Chattopadhyay, Arkadev and Mukhopadhyay, Sagnik},
title = {{Tribes Is Hard in the Message Passing Model}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {224--237},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.224},
URN = {urn:nbn:de:0030-drops-49162},
doi = {10.4230/LIPIcs.STACS.2015.224},
annote = {Keywords: communication complexity, Tribes, information complexity, direct-sum}
}
Document
Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees
Abstract
In a directed graph G with non-correlated edge lengths and costs, the network design problem with bounded distances asks for a cost-minimal spanning subgraph subject to a length bound for all node pairs. We give a bi-criteria (2+\varepsilon,O(n^{0.5+\varepsilon}))-approximation for this problem. This improves on the currently best known linear approximation bound, at the cost of violating the distance bound by a factor of at most 2+\varepsilon.
In the course of proving this result, the related problem of directed shallow-light Steiner trees arises as a subproblem. In the context of directed graphs, approximations to this problem have been elusive. We present the first non-trivial result by proposing a (1+\varepsilon,O(|R|^{\varepsilon}))-ap\-proximation, where R is the set of terminals.
Finally, we show how to apply our results to obtain an (\alpha+\varepsilon,O(n^{0.5+\varepsilon}))-approximation for light-weight directed \alpha-spanners. For this, no non-trivial approximation algorithm has been known before. All running times depends on n and
\varepsilon and are polynomial in n for any fixed \varepsilon>0.
Cite as
Markus Chimani and Joachim Spoerhase. Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 238-248, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{chimani_et_al:LIPIcs.STACS.2015.238,
author = {Chimani, Markus and Spoerhase, Joachim},
title = {{Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {238--248},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.238},
URN = {urn:nbn:de:0030-drops-49170},
doi = {10.4230/LIPIcs.STACS.2015.238},
annote = {Keywords: network design, approximation algorithm, shallow-light spanning trees, spanners}
}
Document
Combinatorial Expressions and Lower Bounds
Abstract
A new paradigm, called combinatorial expressions, for computing functions expressing properties over infinite domains is introduced. The main result is a generic technique, for showing indefinability of
certain functions by the expressions, which uses a result, namely Hales-Jewett theorem, from Ramsey theory. An application of the technique for proving inexpressibility results for logics on metafinite structures is given. Some extensions and normal forms are also presented.
Cite as
Thomas Colcombet and Amaldev Manuel. Combinatorial Expressions and Lower Bounds. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 249-261, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{colcombet_et_al:LIPIcs.STACS.2015.249,
author = {Colcombet, Thomas and Manuel, Amaldev},
title = {{Combinatorial Expressions and Lower Bounds}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {249--261},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.249},
URN = {urn:nbn:de:0030-drops-49181},
doi = {10.4230/LIPIcs.STACS.2015.249},
annote = {Keywords: expressions, lower bound, indefinability}
}
Document
Construction of mu-Limit Sets of Two-dimensional Cellular Automata
Abstract
We prove a characterisation of \mu-limit sets of two-dimensional cellular automata, extending existing results in the one-dimensional case. This sets describe the typical asymptotic behaviour of the cellular automaton, getting rid of exceptional cases, when starting from the uniform measure.
Cite as
Martin Delacourt and Benjamin Hellouin de Ménibus. Construction of mu-Limit Sets of Two-dimensional Cellular Automata. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 262-274, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{delacourt_et_al:LIPIcs.STACS.2015.262,
author = {Delacourt, Martin and Hellouin de M\'{e}nibus, Benjamin},
title = {{Construction of mu-Limit Sets of Two-dimensional Cellular Automata}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {262--274},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.262},
URN = {urn:nbn:de:0030-drops-49197},
doi = {10.4230/LIPIcs.STACS.2015.262},
annote = {Keywords: cellular automata, dynamical systems, mu-limit sets, subshifts, measures}
}
Document
Derandomized Graph Product Results Using the Low Degree Long Code
Abstract
In this paper, we address the question of whether the recent derandomization results obtained by the use of the low-degree long code can be extended to other product settings. We consider two settings: (1) the graph product results of Alon, Dinur, Friedgut and Sudakov [GAFA, 2004] and (2) the "majority is stablest" type of result obtained by Dinur, Mossel and Regev [SICOMP, 2009] and Dinur and Shinkar [In Proc. APPROX, 2010] while studying the hardness of approximate graph coloring.
In our first result, we show that there exists a considerably smaller
subgraph of K_3^{\otimes R} which exhibits the following property
(shown for K_3^{\otimes R} by Alon et al.): independent sets close in
size to the maximum independent set are well approximated by dictators.
The "majority is stablest" type of result of Dinur et al. and Dinur
and Shinkar shows that if there exist two sets of vertices A and B
in K_3^{\otimes R} with very few edges with one endpoint in A and
another in B, then it must be the case that the two sets A and B
share a single influential coordinate. In our second result, we show
that a similar "majority is stablest" statement holds good for a
considerably smaller subgraph of K_3^{\otimes R}. Furthermore using
this result, we give a more efficient reduction from Unique Games
to the graph coloring problem, leading to improved hardness of
approximation results for coloring.
Cite as
Irit Dinur, Prahladh Harsha, Srikanth Srinivasan, and Girish Varma. Derandomized Graph Product Results Using the Low Degree Long Code. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 275-287, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{dinur_et_al:LIPIcs.STACS.2015.275,
author = {Dinur, Irit and Harsha, Prahladh and Srinivasan, Srikanth and Varma, Girish},
title = {{Derandomized Graph Product Results Using the Low Degree Long Code}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {275--287},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.275},
URN = {urn:nbn:de:0030-drops-49200},
doi = {10.4230/LIPIcs.STACS.2015.275},
annote = {Keywords: graph product, derandomization, low degree long code, graph coloring}
}
Document
Space-efficient Basic Graph Algorithms
Abstract
We reconsider basic algorithmic graph problems in a setting where an n-vertex input graph is read-only and the computation must take place in a working memory of O(n) bits or little more than that. For computing connected components and performing breadth-first search, we match
the running times of standard algorithms that have no memory restrictions, for depth-first search and related problems we come within a factor of \Theta(\log\log n), and for computing minimum spanning forests and single-source shortest-paths trees we come close for sparse input graphs.
Cite as
Amr Elmasry, Torben Hagerup, and Frank Kammer. Space-efficient Basic Graph Algorithms. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 288-301, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{elmasry_et_al:LIPIcs.STACS.2015.288,
author = {Elmasry, Amr and Hagerup, Torben and Kammer, Frank},
title = {{Space-efficient Basic Graph Algorithms}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {288--301},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.288},
URN = {urn:nbn:de:0030-drops-49217},
doi = {10.4230/LIPIcs.STACS.2015.288},
annote = {Keywords: graph algorithms, depth-first search, single-source shortest paths, register input model}
}
Document
Pattern Matching with Variables: Fast Algorithms and New Hardness Results
Abstract
A pattern (i. e., a string of variables and terminals) maps to a word, if this is obtained by uniformly replacing the variables by terminal words; deciding this is NP-complete. We present efficient
algorithms\footnote{The computational model we use is the standard unit-cost RAM with logarithmic word size. Also, all logarithms appearing in our time complexity evaluations are in base 2.} that solve this problem for restricted classes of patterns. Furthermore, we show that it is NP-complete to decide, for a given number k and a word w, whether w can be factorised into k distinct factors; this shows that the injective version (i.e., different variables are replaced by different words) of the above matching problem is NP-complete even for very restricted cases.
Cite as
Henning Fernau, Florin Manea, Robert Mercas, and Markus L. Schmid. Pattern Matching with Variables: Fast Algorithms and New Hardness Results. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 302-315, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{fernau_et_al:LIPIcs.STACS.2015.302,
author = {Fernau, Henning and Manea, Florin and Mercas, Robert and Schmid, Markus L.},
title = {{Pattern Matching with Variables: Fast Algorithms and New Hardness Results}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {302--315},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.302},
URN = {urn:nbn:de:0030-drops-49220},
doi = {10.4230/LIPIcs.STACS.2015.302},
annote = {Keywords: combinatorial pattern matching, combinatorics on words, patterns with variables, \$\{cal NP\}\$-complete string problems}
}
Document
Approximating the Generalized Terminal Backup Problem via Half-integral Multiflow Relaxation
Abstract
We consider a network design problem called the generalized terminal backup problem. Whereas earlier work investigated the edge-connectivity constraints only, we consider both edge- and node-connectivity constraints for this problem. A major contribution of this paper is
the development of a strongly polynomial-time 4/3-approximation algorithm for the problem. Specifically, we show that a linear programming relaxation of the problem is half-integral, and that the half-integral optimal solution can be rounded to a 4/3-approximate solution. We also prove that the linear programming relaxation of the problem with the edge-connectivity constraints is equivalent to minimizing the cost of half-integral multiflows that satisfy flow demands given from terminals. This observation implies a strongly polynomial-time algorithm for computing a minimum cost half-integral multiflow under flow demand constraints.
Cite as
Takuro Fukunaga. Approximating the Generalized Terminal Backup Problem via Half-integral Multiflow Relaxation. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 316-328, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{fukunaga:LIPIcs.STACS.2015.316,
author = {Fukunaga, Takuro},
title = {{Approximating the Generalized Terminal Backup Problem via Half-integral Multiflow Relaxation}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {316--328},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.316},
URN = {urn:nbn:de:0030-drops-49236},
doi = {10.4230/LIPIcs.STACS.2015.316},
annote = {Keywords: survivable network design, multiflow, LP rounding}
}
Document
On Matrix Powering in Low Dimensions
Abstract
We investigate the Matrix Powering Positivity Problem, PosMatPow: given an m X m square integer matrix M, a linear function f: Z^{m X m} -> Z with integer coefficients, and a positive integer n (encoded in binary), determine whether f(M^n) \geq 0. We show that for fixed dimensions m of 2 and 3, this problem is decidable in polynomial time.
Cite as
Esther Galby, Joël Ouaknine, and James Worrell. On Matrix Powering in Low Dimensions. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 329-340, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{galby_et_al:LIPIcs.STACS.2015.329,
author = {Galby, Esther and Ouaknine, Jo\"{e}l and Worrell, James},
title = {{On Matrix Powering in Low Dimensions}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {329--340},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.329},
URN = {urn:nbn:de:0030-drops-49240},
doi = {10.4230/LIPIcs.STACS.2015.329},
annote = {Keywords: matrix powering, complexity, Baker's theorem}
}
Document
The Complexity of Recognizing Unique Sink Orientations
Abstract
Given a Boolean Circuit with n inputs and n outputs, we want to decide if it represents a Unique Sink Orientation (USO). USOs are useful combinatorial objects that serve as abstraction of many relevant optimization problems. We prove that recognizing a USO is coNP-complete. However, the situation appears to be more complicated for recognizing acyclic USOs. Firstly, we give a construction to prove that there exist cyclic USOs where the smallest cycle is of superpolynomial size. This implies that the straightforward representation of a cycle (i.e. by a list of vertices) does not make up for a coNP certificate. Inspired by this fact, we investigate the connection of recognizing an acyclic USO to PSPACE and we prove that the problem is PSPACE-complete.
Cite as
Bernd Gärtner and Antonis Thomas. The Complexity of Recognizing Unique Sink Orientations. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 341-353, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{gartner_et_al:LIPIcs.STACS.2015.341,
author = {G\"{a}rtner, Bernd and Thomas, Antonis},
title = {{The Complexity of Recognizing Unique Sink Orientations}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {341--353},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.341},
URN = {urn:nbn:de:0030-drops-49252},
doi = {10.4230/LIPIcs.STACS.2015.341},
annote = {Keywords: complexity, recognizing, unique sink orientations, coNP, PSPACE}
}
Document
New Geometric Representations and Domination Problems on Tolerance and Multitolerance Graphs
Abstract
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict.
In one of the most natural generalizations of tolerance graphs with direct applications in the comparison of DNA sequences from different organisms, namely multitolerance graphs, two tolerances are allowed
for each interval - one from the left and one from the right side.
Several efficient algorithms for optimization problems that are NP-hard in general graphs have been designed for tolerance and multitolerance graphs. In spite of this progress, the complexity status of some fundamental algorithmic problems on tolerance and multitolerance graphs, such as the dominating set problem, remained unresolved until now,
three decades after the introduction of tolerance graphs. In this article we introduce two new geometric representations for tolerance and multitolerance graphs, given by points and line segments in the plane.
Apart from being important on their own, these new representations prove to be a powerful tool for deriving both hardness results and polynomial time algorithms. Using them, we surprisingly prove that the dominating set problem can be solved in polynomial time on tolerance graphs and that it is APX-hard on multitolerance graphs, solving thus a longstanding open problem. This problem is the first one that has been discovered with a different complexity status in these two graph classes. Furthermore we present an algorithm that solves the independent dominating set problem on multitolerance graphs in polynomial time,
thus demonstrating the potential of this new representation for further exploitation via sweep line algorithms.
Cite as
Archontia C. Giannopoulou and George B. Mertzios. New Geometric Representations and Domination Problems on Tolerance and Multitolerance Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 354-366, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{giannopoulou_et_al:LIPIcs.STACS.2015.354,
author = {Giannopoulou, Archontia C. and Mertzios, George B.},
title = {{New Geometric Representations and Domination Problems on Tolerance and Multitolerance Graphs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {354--366},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.354},
URN = {urn:nbn:de:0030-drops-49268},
doi = {10.4230/LIPIcs.STACS.2015.354},
annote = {Keywords: tolerance graphs, multitolerance graphs, geometric representation, dominating set problem, polynomial time algorithm, APX-hard}
}
Document
Comparing 1D and 2D Real Time on Cellular Automata
Abstract
We study the influence of the dimension of cellular automata (CA) for real time language recognition of one-dimensional languages with parallel input. Specifically, we focus on the question of determining whether every language that can be recognized in real time on a 2-dimensional CA working on the Moore neighborhood can also be recognized in real time by a 1-dimensional CA working on the standard two-way neighborhood. We show that 2-dimensional CA in real time can perform a linear number of simulations of a 1-dimensional real time CA. If the two classes are equal then the number of simulated instances can be polynomial.
Cite as
Anaël Grandjean and Victor Poupet. Comparing 1D and 2D Real Time on Cellular Automata. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 367-378, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{grandjean_et_al:LIPIcs.STACS.2015.367,
author = {Grandjean, Ana\"{e}l and Poupet, Victor},
title = {{Comparing 1D and 2D Real Time on Cellular Automata}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {367--378},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.367},
URN = {urn:nbn:de:0030-drops-49275},
doi = {10.4230/LIPIcs.STACS.2015.367},
annote = {Keywords: Cellular automata, real time, language recognition}
}
Document
Tropical Effective Primary and Dual Nullstellens"atze
Abstract
Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties and algebraic curves from the computational point of view. This makes it important to study both mathematical and computational aspects of tropical polynomials.
In this paper we prove tropical Nullstellensatz and moreover we show effective formulation of this theorem. Nullstellensatz is a next natural step in building algebraic theory of tropical polynomials and
effective version is relevant for computational aspects of this field.
Cite as
Dima Grigoriev and Vladimir V. Podolskii. Tropical Effective Primary and Dual Nullstellens"atze. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 379-391, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{grigoriev_et_al:LIPIcs.STACS.2015.379,
author = {Grigoriev, Dima and Podolskii, Vladimir V.},
title = {{Tropical Effective Primary and Dual Nullstellens"atze}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {379--391},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.379},
URN = {urn:nbn:de:0030-drops-49286},
doi = {10.4230/LIPIcs.STACS.2015.379},
annote = {Keywords: tropical algebra, tropical geometry, Nullstellensatz}
}
Document
Upper Tail Estimates with Combinatorial Proofs
Abstract
We study generalisations of a simple, combinatorial proof of a Chernoff bound similar to the one by Impagliazzo and Kabanets (RANDOM, 2010).
In particular, we prove a randomized version of the hitting property of expander random walks and use it to obtain an optimal expander random
walk concentration bound settling a question asked by Impagliazzo and Kabanets.
Next, we obtain an upper tail bound for polynomials with input variables in [0, 1] which are not necessarily independent, but obey a certain condition inspired by Impagliazzo and Kabanets. The resulting bound
is applied by Holenstein and Sinha (FOCS, 2012) in the proof of a lower bound for the number of calls in a black-box construction of a pseudorandom generator from a one-way function.
We also show that the same technique yields the upper tail bound for the number of copies of a fixed graph in an Erdös–Rényi random graph,
matching the one given by Janson, Oleszkiewicz, and Rucinski (Israel J. Math, 2002).
Cite as
Jan Hazla and Thomas Holenstein. Upper Tail Estimates with Combinatorial Proofs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 392-405, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{hazla_et_al:LIPIcs.STACS.2015.392,
author = {Hazla, Jan and Holenstein, Thomas},
title = {{Upper Tail Estimates with Combinatorial Proofs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {392--405},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.392},
URN = {urn:nbn:de:0030-drops-49291},
doi = {10.4230/LIPIcs.STACS.2015.392},
annote = {Keywords: concentration bounds, expander random walks, polynomial concentration}
}
Document
Minimum Cost Flows in Graphs with Unit Capacities
Abstract
We consider the minimum cost flow problem on graphs with unit capacities and its special cases. In previous studies, special purpose algorithms exploiting the fact that capacities are one have been developed.
In contrast, for maximum flow with unit capacities, the best bounds are proven for slight modifications of classical blocking flow and push-relabel algorithms.
In this paper we show that the classical cost scaling algorithms of Goldberg and Tarjan (for general integer capacities) applied to a problem with unit capacities achieve or improve the best known bounds.
For weighted bipartite matching we establish a bound of O(\sqrt{rm}\log C) on a slight variation of this algorithm. Here r is the size of the smaller side of the bipartite graph, m is the number of edges, and C is the largest absolute value of an arc-cost. This simplifies a result of [Duan et al. 2011] and improves the bound, answering an open question of [Tarjan and Ramshaw 2012]. For graphs with unit vertex capacities we establish a novel O(\sqrt{n}m\log(nC)) bound. We also give the first cycle canceling algorithm for minimum cost flow with unit capacities. The algorithm naturally generalizes the single source shortest path algorithm of [Goldberg 1995].
Cite as
Andrew V. Goldberg, Haim Kaplan, Sagi Hed, and Robert E. Tarjan. Minimum Cost Flows in Graphs with Unit Capacities. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 406-419, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{goldberg_et_al:LIPIcs.STACS.2015.406,
author = {Goldberg, Andrew V. and Kaplan, Haim and Hed, Sagi and Tarjan, Robert E.},
title = {{Minimum Cost Flows in Graphs with Unit Capacities}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {406--419},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.406},
URN = {urn:nbn:de:0030-drops-49304},
doi = {10.4230/LIPIcs.STACS.2015.406},
annote = {Keywords: minimum cost flow, bipartite matching, unit capacity, cost scaling}
}
Document
Inductive Inference and Reverse Mathematics
Abstract
The present work investigates inductive inference from the perspective
of reverse mathematics. Reverse mathematics is a framework which relates
the proof strength of theorems and axioms throughout many areas of
mathematics in an interdisciplinary way. The present work looks at
basic notions of learnability including Angluin's tell-tale condition and its variants for learning in the limit and for conservative learning. Furthermore, the more general criterion of partial learning is investigated. These notions are studied in the reverse mathematics context for uniformly and weakly represented families of languages. The results are stated in terms of axioms referring to domination and induction strength.
Cite as
Rupert Hölzl, Sanjay Jain, and Frank Stephan. Inductive Inference and Reverse Mathematics. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 420-433, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{holzl_et_al:LIPIcs.STACS.2015.420,
author = {H\"{o}lzl, Rupert and Jain, Sanjay and Stephan, Frank},
title = {{Inductive Inference and Reverse Mathematics}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {420--433},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.420},
URN = {urn:nbn:de:0030-drops-49324},
doi = {10.4230/LIPIcs.STACS.2015.420},
annote = {Keywords: reverse mathematics, recursion theory, inductive inference, learning from positive data}
}
Document
Dynamic Planar Embeddings of Dynamic Graphs
Abstract
We present an algorithm to support the dynamic embedding in the plane
of a dynamic graph. An edge can be inserted across a face between two vertices on the boundary (we call such a vertex pair linkable), and edges can be deleted. The planar embedding can also be changed locally by flipping components that are connected to the rest of the graph by at most two vertices. Given vertices u,v, linkable(u,v) decides whether u and v are linkable, and if so, returns a list of suggestions for the placement of (u,v) in the embedding. For non-linkable vertices u,v, we define a new query, one-flip-linkable(u,v) providing a suggestion for a flip that will make them linkable if one exists. We will support all updates and queries in O(log^2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph.
Our new algorithm is simpler, exploiting that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant
interaction between top trees over the two trees via their common Euler tour.
Cite as
Jacob Holm and Eva Rotenberg. Dynamic Planar Embeddings of Dynamic Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 434-446, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{holm_et_al:LIPIcs.STACS.2015.434,
author = {Holm, Jacob and Rotenberg, Eva},
title = {{Dynamic Planar Embeddings of Dynamic Graphs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {434--446},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.434},
URN = {urn:nbn:de:0030-drops-49319},
doi = {10.4230/LIPIcs.STACS.2015.434},
annote = {Keywords: dynamic graphs, planar embeddings, data structures}
}
Document
On the Information Carried by Programs about the Objects They Compute
Abstract
In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an infinite tape. What additional information do programs provide? We characterize this additional information to be any upper bound on the Kolmogorov complexity of the object. Hence we identify the exact relationship between Markov-computability and Type-2-computability. We then use this relationship to obtain several results characterizing the computational and topological structure of Markov-semidecidable sets.
Cite as
Mathieu Hoyrup and Cristóbal Rojas. On the Information Carried by Programs about the Objects They Compute. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 447-459, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{hoyrup_et_al:LIPIcs.STACS.2015.447,
author = {Hoyrup, Mathieu and Rojas, Crist\'{o}bal},
title = {{On the Information Carried by Programs about the Objects They Compute}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {447--459},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.447},
URN = {urn:nbn:de:0030-drops-49337},
doi = {10.4230/LIPIcs.STACS.2015.447},
annote = {Keywords: Markov-computable, representation, Kolmogorov complexity, Ershov topology}
}
Document
Communication Complexity of Approximate Matching in Distributed Graphs
Abstract
In this paper we consider the communication complexity of approximation algorithms for maximum matching in a graph in the message-passing model of distributed computation. The input graph consists of n vertices and edges partitioned over a set of k sites. The output is an \alpha-approximate maximum matching in the input graph which has to be reported by one of the sites. We show a lower bound on the communication complexity of \Omega(\alpha^2 k n) and show that it is tight up to poly-logarithmic factors. This lower bound also applies to other combinatorial problems on graphs in the message-passing computation model, including max-flow and graph sparsification.
Cite as
Zengfeng Huang, Bozidar Radunovic, Milan Vojnovic, and Qin Zhang. Communication Complexity of Approximate Matching in Distributed Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 460-473, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{huang_et_al:LIPIcs.STACS.2015.460,
author = {Huang, Zengfeng and Radunovic, Bozidar and Vojnovic, Milan and Zhang, Qin},
title = {{Communication Complexity of Approximate Matching in Distributed Graphs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {460--473},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.460},
URN = {urn:nbn:de:0030-drops-49348},
doi = {10.4230/LIPIcs.STACS.2015.460},
annote = {Keywords: approximate maximum matching, distributed computation, communication complexity}
}
Document
Stochastic Scheduling of Heavy-tailed Jobs
Abstract
We revisit the classical stochastic scheduling problem of nonpreemptively scheduling n jobs so as to minimize total completion time on m identical machines, P \mid \mid \mathbb{E} \sum C_j in the standard 3-field scheduling notation. Previously it was only known how to obtain reasonable approximation if jobs sizes have low variability. However, distributions commonly arising in practice have high variability, and the upper bounds on the approximation ratio for the previous algorithms for such distributions can be even inverse-polynomial in the maximum possible job size. We start by showing that
the natural list scheduling algorithm Shortest Expected Processing Time (SEPT) has a bad approximation ratio for high variability jobs. We observe that a simple randomized rounding of a natural linear programming relaxation is a (1+\epsilon)-machine O(1)-approximation assuming the number of machines is at least logarithmic in the number of jobs. Turning to the case of a modest number of machines, we develop a list scheduling algorithm that is O(\log^2 n + m \log n)-approximate. Our results together imply a (1+\epsilon)-machine O(\log^2 n )-approximation for an arbitrary number of machines. Intuitively our list scheduling algorithm finds an ordering that not only takes the expected size of a job into account, but also takes into account the probability that job will be big.
Cite as
Sungjin Im, Benjamin Moseley, and Kirk Pruhs. Stochastic Scheduling of Heavy-tailed Jobs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 474-486, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{im_et_al:LIPIcs.STACS.2015.474,
author = {Im, Sungjin and Moseley, Benjamin and Pruhs, Kirk},
title = {{Stochastic Scheduling of Heavy-tailed Jobs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {474--486},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.474},
URN = {urn:nbn:de:0030-drops-49359},
doi = {10.4230/LIPIcs.STACS.2015.474},
annote = {Keywords: stochastic scheduling, completion time, approximation}
}
Document
On Finding the Adams Consensus Tree
Abstract
This paper presents a fast algorithm for finding the Adams consensus tree of a set of conflicting phylogenetic trees with identical leaf labels, for the first time improving the time complexity of a widely used algorithm invented by Adams in 1972 [1]. Our algorithm applies
the centroid path decomposition technique [9] in a new way to traverse the input trees' centroid paths in unison, and runs in O(k n \log n) time, where k is the number of input trees and n is the size of the leaf label set. (In comparison, the old algorithm from 1972 has a worst-case running time of O(k n^2).) For the special case of k = 2, an even faster algorithm running in O(n \cdot \frac{\log n}{\log\log n}) time is provided, which relies on an extension of the wavelet tree-based technique by Bose et al. [6] for orthogonal range counting on a grid.
Our extended wavelet tree data structure also supports truncated
range maximum queries efficiently and may be of independent interest to algorithm designers.
Cite as
Jesper Jansson, Zhaoxian Li, and Wing-Kin Sung. On Finding the Adams Consensus Tree. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 487-499, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{jansson_et_al:LIPIcs.STACS.2015.487,
author = {Jansson, Jesper and Li, Zhaoxian and Sung, Wing-Kin},
title = {{On Finding the Adams Consensus Tree}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {487--499},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.487},
URN = {urn:nbn:de:0030-drops-49364},
doi = {10.4230/LIPIcs.STACS.2015.487},
annote = {Keywords: phylogenetic tree, Adams consensus, centroid path, wavelet tree}
}
Document
Flip Distance Is in FPT Time O(n+ k * c^k)
Abstract
Let T be a triangulation of a set P of n points in the plane, and let e be an edge shared by two triangles in T such that the quadrilateral Q formed by these two triangles is convex. A flip of e is the operation of replacing e by the other diagonal of Q to obtain a new triangulation of P from T. The flip distance between two triangulations of P is the minimum number of flips needed to transform one triangulation into the other. The Flip Distance problem asks if the flip distance between two given triangulations of P is k, for some given k \in \mathbb{N}. It is a fundamental and a challenging problem.
In this paper we present an algorithm for the Flip Distance problem that
runs in time O(n + k \cdot c^{k}), for a constant c \leq 2 \cdot
14^11, which implies that the problem is fixed-parameter tractable. The
NP-hardness reduction for the Flip Distance problem given by Lubiw
and Pathak can be used to show that, unless the exponential-time hypothesis (ETH) fails, the Flip Distance problem cannot be solved in time O^*(2^o(k)). Therefore, one cannot expect an asymptotic improvement in the exponent of the running time of our algorithm.
Cite as
Iyad Kanj and Ge Xia. Flip Distance Is in FPT Time O(n+ k * c^k). In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 500-512, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{kanj_et_al:LIPIcs.STACS.2015.500,
author = {Kanj, Iyad and Xia, Ge},
title = {{Flip Distance Is in FPT Time O(n+ k * c^k)}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {500--512},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.500},
URN = {urn:nbn:de:0030-drops-49371},
doi = {10.4230/LIPIcs.STACS.2015.500},
annote = {Keywords: triangulations, flip distance, parameterized algorithms}
}
Document
New Pairwise Spanners
Abstract
Let G = (V,E) be an undirected unweighted graph on n vertices. A subgraph H of G is called an (all-pairs) purely additive spanner with stretch \beta if for every (u,v) \in V \times V, \mathsf{dist}_H(u,v) \le \mathsf{dist}_G(u,v) + \beta. The problem of computing sparse spanners with small stretch \beta is well-studied. Here we consider the following relaxation: we are given \p\subseteq V \times V and we seek a sparse subgraph H where \mathsf{dist}_H(u,v)\le \mathsf{dist}_G(u,v) + \beta for each (u,v) \in \p. Such a subgraph is called a pairwise spanner with additive stretch \beta and our goal is to construct
such subgraphs that are sparser than all-pairs spanners with the same stretch. We show sparse pairwise spanners with additive stretch 4 and with additive stretch 6. We also consider the following special cases: \p = S \times V and \p = S \times T, where S\subseteq V and T\subseteq V, and show sparser pairwise spanners for these cases.
Cite as
Telikepalli Kavitha. New Pairwise Spanners. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 513-526, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{kavitha:LIPIcs.STACS.2015.513,
author = {Kavitha, Telikepalli},
title = {{New Pairwise Spanners}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {513--526},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.513},
URN = {urn:nbn:de:0030-drops-49381},
doi = {10.4230/LIPIcs.STACS.2015.513},
annote = {Keywords: undirected graphs, spanners, approximate distances, additive stretch}
}
Document
Multi-k-ic Depth Three Circuit Lower Bound
Abstract
In a multi-k-ic depth three circuit every variable appears in at most k of the linear polynomials in every product gate of the circuit. This model is a natural generalization of multilinear depth three circuits that allows the formal degree of the circuit to exceed the number of underlying variables (as the formal degree of a multi-k-ic depth three circuit can be kn where n is the number of variables). The problem of proving lower bounds for depth three circuits with high formal degree has gained in importance following a work by Gupta, Kamath, Kayal and Saptharishi [7] on depth reduction to high formal degree depth three circuits. In this work, we show an exponential lower bound for multi-k-ic depth three circuits for any arbitrary constant k.
Cite as
Neeraj Kayal and Chandan Saha. Multi-k-ic Depth Three Circuit Lower Bound. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 527-539, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{kayal_et_al:LIPIcs.STACS.2015.527,
author = {Kayal, Neeraj and Saha, Chandan},
title = {{Multi-k-ic Depth Three Circuit Lower Bound}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {527--539},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.527},
URN = {urn:nbn:de:0030-drops-49395},
doi = {10.4230/LIPIcs.STACS.2015.527},
annote = {Keywords: arithmetic circuits, multilinear circuits, depth three circuits, lower bound, individual degree}
}
Document
Automorphism Groups of Geometrically Represented Graphs
Abstract
Interval graphs are intersection graphs of closed intervals and circle graphs are intersection graphs of chords of a circle. We study automorphism groups of these graphs. We show that interval graphs have the same automorphism groups as trees, and circle graphs have the same
as pseudoforests, which are graphs with at most one cycle in every connected component.
Our technique determines automorphism groups for classes with a
strong structure of all geometric representations, and it can be applied to other graph classes. Our results imply polynomial-time algorithms for computing automorphism groups in term of group products.
Cite as
Pavel Klavík and Peter Zeman. Automorphism Groups of Geometrically Represented Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 540-553, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{klavik_et_al:LIPIcs.STACS.2015.540,
author = {Klav{\'\i}k, Pavel and Zeman, Peter},
title = {{Automorphism Groups of Geometrically Represented Graphs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {540--553},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.540},
URN = {urn:nbn:de:0030-drops-49408},
doi = {10.4230/LIPIcs.STACS.2015.540},
annote = {Keywords: automorphism group, geometric intersection graph, interval graph, circle graph}
}
Document
Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs
Abstract
In correlation clustering, the input is a graph with edge-weights, where every edge is labelled either + or - according to similarity of its endpoints. The goal is to produce a partition of the vertices that disagrees with the edge labels as little as possible.
In two-edge-connected augmentation, the input is a graph with edge-weights and a subset R of edges of the graph. The goal is to produce a minimum weight subset S of edges of the graph, such that for every edge in R, its endpoints are two-edge-connected in R\cup S.
For planar graphs, we prove that correlation clustering reduces to two-edge-connected augmentation, and that both problems have a polynomial-time approximation scheme.
Cite as
Philip N. Klein, Claire Mathieu, and Hang Zhou. Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 554-567, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{klein_et_al:LIPIcs.STACS.2015.554,
author = {Klein, Philip N. and Mathieu, Claire and Zhou, Hang},
title = {{Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {554--567},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.554},
URN = {urn:nbn:de:0030-drops-49411},
doi = {10.4230/LIPIcs.STACS.2015.554},
annote = {Keywords: correlation clustering, two-edge-connected augmentation, polynomial-time approximation scheme, planar graphs}
}
Document
Extended Formulation Lower Bounds via Hypergraph Coloring?
Abstract
Exploring the power of linear programming for combinatorial optimization
problems has been recently receiving renewed attention after a series of
breakthrough impossibility results. From an algorithmic perspective, the
related questions concern whether there are compact formulations even for problems that are known to admit polynomial-time algorithms.
We propose a framework for proving lower bounds on the size of extended
formulations. We do so by introducing a specific type of extended relaxations that we call product relaxations and is motivated by the study of the Sherali-Adams (SA) hierarchy. Then we show that for every approximate extended formulation of a polytope P, there is a product relaxation that has the same size and is at least as strong. We provide a methodology for proving lower bounds on the size of approximate product relaxations by lower bounding the chromatic number of an underlying hypergraph, whose vertices correspond to gap-inducing vectors.
We extend the definition of product relaxations and our methodology to mixed integer sets. However in this case we are able to show that mixed product relaxations are at least as powerful as a special family of extended formulations. As an application of our method we show an exponential lower bound on the size of approximate mixed product relaxations for the metric capacitated facility location problem Cfl, a problem which seems to be intractable for linear programming as far as constant-gap compact formulations are concerned. Our lower bound implies an unbounded integrality gap for Cfl at Theta({N}) levels of the universal SA hierarchy which is independent of the starting relaxation; we only require that the starting relaxation has size 2^o(N), where N is the number of facilities in the instance. This proof yields the first such tradeoff for an SA procedure that is independent of the initial relaxation.
Cite as
Stavros G. Kolliopoulos and Yannis Moysoglou. Extended Formulation Lower Bounds via Hypergraph Coloring?. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 568-581, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{kolliopoulos_et_al:LIPIcs.STACS.2015.568,
author = {Kolliopoulos, Stavros G. and Moysoglou, Yannis},
title = {{Extended Formulation Lower Bounds via Hypergraph Coloring?}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {568--581},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.568},
URN = {urn:nbn:de:0030-drops-49429},
doi = {10.4230/LIPIcs.STACS.2015.568},
annote = {Keywords: linear programming, extended formulations, inapproximability, facility location}
}
Document
Lempel-Ziv Factorization May Be Harder Than Computing All Runs
Abstract
The complexity of computing the Lempel-Ziv decomposition and the set of all runs (= maximal repetitions) is studied in the decision tree model of computation over ordered alphabet. It is known that both these problems can be solved by RAM algorithms in O(n\log\sigma) time, where n is the length of the input string and \sigma is the number of distinct letters in it. We prove an \Omega(n\log\sigma) lower bound on the number of comparisons required to construct the Lempel-Ziv decomposition and thereby conclude that a popular technique of computation of runs using the Lempel-Ziv decomposition cannot achieve an o(n\log\sigma) time bound. In contrast with this, we exhibit an O(n) decision tree algorithm finding all runs in a string. Therefore, in the decision tree model the runs problem is easier than the Lempel-Ziv decomposition. Thus we support the conjecture that there is a linear RAM algorithm finding all runs.
Cite as
Dmitry Kosolobov. Lempel-Ziv Factorization May Be Harder Than Computing All Runs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 582-593, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{kosolobov:LIPIcs.STACS.2015.582,
author = {Kosolobov, Dmitry},
title = {{Lempel-Ziv Factorization May Be Harder Than Computing All Runs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {582--593},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.582},
URN = {urn:nbn:de:0030-drops-49438},
doi = {10.4230/LIPIcs.STACS.2015.582},
annote = {Keywords: Lempel-Ziv factorization, runs, repetitions, decision tree, lower bounds}
}
Document
Visibly Counter Languages and Constant Depth Circuits
Abstract
We examine visibly counter languages, which are languages recognized by visibly counter automata (a.k.a. input driven counter automata). We are able to effectively characterize the visibly counter languages in AC^0 and show that they are contained in FO[+].
Cite as
Andreas Krebs, Klaus-Jörn Lange, and Michael Ludwig. Visibly Counter Languages and Constant Depth Circuits. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 594-607, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{krebs_et_al:LIPIcs.STACS.2015.594,
author = {Krebs, Andreas and Lange, Klaus-J\"{o}rn and Ludwig, Michael},
title = {{Visibly Counter Languages and Constant Depth Circuits}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {594--607},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.594},
URN = {urn:nbn:de:0030-drops-49447},
doi = {10.4230/LIPIcs.STACS.2015.594},
annote = {Keywords: visibly counter automata, constant depth circuits, AC0, FO\lbrack+\rbrack}
}
Document
Optimal Decremental Connectivity in Planar Graphs
Abstract
We show an algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions. Our algorithm may answer connectivity queries of the form 'Are vertices u and v connected with a path?' in constant time. The queries can be intermixed with any sequence of edge deletions, and the algorithm handles all updates in O(n) time. This results improves over previously known O(n \log n) time algorithm.
Cite as
Jakub Lacki and Piotr Sankowski. Optimal Decremental Connectivity in Planar Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 608-621, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{lacki_et_al:LIPIcs.STACS.2015.608,
author = {Lacki, Jakub and Sankowski, Piotr},
title = {{Optimal Decremental Connectivity in Planar Graphs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {608--621},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.608},
URN = {urn:nbn:de:0030-drops-49457},
doi = {10.4230/LIPIcs.STACS.2015.608},
annote = {Keywords: decremental connectivity, planar graphs, dynamic connectivity, algorithms}
}
Document
Testing Small Set Expansion in General Graphs
Abstract
We consider the problem of testing small set expansion for general graphs. A graph G is a (k,\phi)-expander if every subset of volume at most k has conductance at least \phi. Small set expansion has recently received significant attention due to its close connection to the unique games conjecture, the local graph partitioning algorithms and locally testable codes.
We give testers with two-sided error and one-sided error in the \adjacency list model that allows degree and neighbor queries to the oracle of the input graph. The testers take as input an n-vertex graph G, a volume bound k, an expansion bound \phi and a distance parameter \varepsilon>0. For the two-sided error tester, with probability at least 2/3, it accepts the graph if it is a (k,\phi)-expander and rejects the graph if it is \varepsilon-far from any (k^*,\phi^*)-expander, where k^*=\Theta(k\varepsilon) and \phi^*=\Theta(\frac{\phi^4}{\min\{\log(4m/k),\log n\}\cdot(\ln k)}). The query complexity and running time of the tester are \widetilde{O}(\sqrt{m}\phi^{-4}\varepsilon^{-2}), where m is the number of edges of the graph. For the one-sided error tester, it accepts every (k,\phi)-expander, and with probability at least 2/3, rejects every graph that is \varepsilon-far from (k^*,\phi^*)-expander, where k^*=O(k^{1-\xi}) and \phi^*=O(\xi\phi^2) for any 0<\xi<1. The query complexity and running time of this tester are \widetilde{O}(\sqrt{\frac{n}{\varepsilon^3}}+\frac{k}{\varepsilon \phi^4}).
We also give a two-sided error tester in the \textit{rotation map} model that allows \textit{(neighbor, index)} queries and degree queries. This tester has asymptotically almost the same query complexity and running time as the two-sided error tester in the adjacency list model, but has a better performance: it can distinguish any $(k,\phi)$-expander from graphs that are $\varepsilon$-far from $(k^*,\phi^*)$-expanders, where $k^*=\Theta(k\varepsilon)$ and $\phi^*=\Theta(\frac{\phi^2}{\min\{\log(4m/k),\log n\}\cdot(\ln k)})$.
In our analysis, we introduce a new graph product called \textit{non-uniform replacement product} that transforms a general graph into a bounded degree graph, and approximately preserves the expansion profile as well as the corresponding spectral property.
Cite as
Angsheng Li and Pan Peng. Testing Small Set Expansion in General Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 622-635, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{li_et_al:LIPIcs.STACS.2015.622,
author = {Li, Angsheng and Peng, Pan},
title = {{Testing Small Set Expansion in General Graphs}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {622--635},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.622},
URN = {urn:nbn:de:0030-drops-49461},
doi = {10.4230/LIPIcs.STACS.2015.622},
annote = {Keywords: graph property testing, small set expansion, random walks, spectral graph theory}
}
Document
Paid Exchanges are Worth the Price
Abstract
We consider the list update problem as defined in the seminal work on competitive analysis by Sleator and Tarjan [12]. In this problem, a sequence of requests, consisting of items to access in a linked list, is given. After an item is accessed it can be moved to any position forward in the list at no cost (free exchange), and, at any time, any two adjacent items can be swapped at a cost of 1 (paid exchange). The cost to access an item is its current position in the list. The goal is to dynamically rearrange the list so as to minimize the total cost (accrued from accesses and exchanges) over the request sequence.
We show a lower bound of 12/11 on the worst-case ratio between the performance of an (offline) optimal algorithm that can only perform free exchanges and that of an (offline) optimal algorithm that can perform both paid and free exchanges. This answers an outstanding question that has been open since 1996 [10].
Cite as
Alejandro López-Ortiz, Marc P. Renault, and Adi Rosén. Paid Exchanges are Worth the Price. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 636-648, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{lopezortiz_et_al:LIPIcs.STACS.2015.636,
author = {L\'{o}pez-Ortiz, Alejandro and Renault, Marc P. and Ros\'{e}n, Adi},
title = {{Paid Exchanges are Worth the Price}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {636--648},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.636},
URN = {urn:nbn:de:0030-drops-49476},
doi = {10.4230/LIPIcs.STACS.2015.636},
annote = {Keywords: list update problem, online computation, online algorithms, competitive analysis, lower bounds}
}
Document
Undecidability in Binary Tag Systems and the Post Correspondence Problem for Five Pairs of Words
Abstract
Since Cocke and Minsky proved 2-tag systems universal, they have been extensively used to prove the universality of numerous computational models. Unfortunately, all known algorithms give universal 2-tag systems that have a large number of symbols. In this work, tag systems with only 2 symbols (the minimum possible) are proved universal via an intricate construction showing that they simulate cyclic tag systems. We immediately find applications of our result. We reduce the halting problem for binary tag systems to the Post correspondence problem for 5 pairs of words. This improves on 7 pairs, the previous bound for undecidability in this problem. Following our result, only the cases for 3 and 4 pairs of words remains open, as the problem is known to be decidable for 2 pairs. In a further application, we apply the reductions of Vesa Halava and others to show that the matrix mortality problem is undecidable for sets with six 3 x 3 matrices and for sets with two 18 x 18 matrices. The previous bounds for the undecidability in this problem was seven 3 x 3 matrices and two 21 x 21 matrices.
Cite as
Turlough Neary. Undecidability in Binary Tag Systems and the Post Correspondence Problem for Five Pairs of Words. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 649-661, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{neary:LIPIcs.STACS.2015.649,
author = {Neary, Turlough},
title = {{Undecidability in Binary Tag Systems and the Post Correspondence Problem for Five Pairs of Words}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {649--661},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.649},
URN = {urn:nbn:de:0030-drops-49486},
doi = {10.4230/LIPIcs.STACS.2015.649},
annote = {Keywords: tag system, Post correspondence problem, undecidability}
}
Document
Separation and the Successor Relation
Abstract
We investigate two problems for a class C of regular word languages. The
C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the second. These problems are considered as means to obtain a deep understanding of the class C.
It is usual for such classes to be defined by logical formalisms. Logics are often built on top of each other, by adding new predicates. A natural construction is to enrich a logic with the successor relation. In this paper, we obtain new and simple proofs of two transfer results: we show that for suitable logically defined classes, the membership, resp. the separation problem for a class enriched with the successor relation reduces to the same problem for the original class.
Our reductions work both for languages of finite words and infinite words. The proofs are mostly self-contained, and only require a basic background on regular languages. This paper therefore gives simple proofs of results that were considered as difficult, such as the decidability of the membership problem for the levels 1, 3/2, 2 and 5/2 of the dot-depth hierarchy.
Cite as
Thomas Place and Marc Zeitoun. Separation and the Successor Relation. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 662-675, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{place_et_al:LIPIcs.STACS.2015.662,
author = {Place, Thomas and Zeitoun, Marc},
title = {{Separation and the Successor Relation}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {662--675},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.662},
URN = {urn:nbn:de:0030-drops-49499},
doi = {10.4230/LIPIcs.STACS.2015.662},
annote = {Keywords: separation problem, regular word languages, logics, decidable characterizations, semidirect product}
}
Document
Computing 2-Walks in Polynomial Time
Abstract
A 2-walk of a graph is a walk visiting every vertex at least once and at most twice. By generalizing decompositions of Tutte and Thomassen, Gao, Richter and Yu proved that every 3-connected planar graph contains a closed 2-walk such that all vertices visited twice are contained in 3-separators. This seminal result generalizes Tutte's theorem that every 4-connected planar graph is Hamiltonian as well as Barnette's theorem that every 3-connected planar graph has a spanning tree with maximum degree at most 3. The algorithmic challenge of finding such a closed 2-walk is to overcome big overlapping subgraphs in the decomposition, which are also inherent in Tutte's and Thomassen's decompositions.
We solve this problem by extending the decomposition of Gao, Richter and Yu in such a way that all pieces, in which the graph is decomposed into, are edge-disjoint. This implies the first polynomial-time algorithm that computes the closed 2-walk mentioned above.
Cite as
Andreas Schmid and Jens M. Schmidt. Computing 2-Walks in Polynomial Time. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 676-688, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{schmid_et_al:LIPIcs.STACS.2015.676,
author = {Schmid, Andreas and Schmidt, Jens M.},
title = {{Computing 2-Walks in Polynomial Time}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {676--688},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.676},
URN = {urn:nbn:de:0030-drops-49502},
doi = {10.4230/LIPIcs.STACS.2015.676},
annote = {Keywords: algorithms and data structures, 2-walks, 3-connected planar graphs, Tutte paths, 3-trees}
}
Document
Towards an Isomorphism Dichotomy for Hereditary Graph Classes
Abstract
In this paper we resolve the complexity of the isomorphism problem on
all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and algorithmic analysis of graphs. First, we develop a methodology to show isomorphism completeness of the isomorphism problem on graph classes by providing a general framework unifying various reduction techniques. Second, we generalize the concept of the modular decomposition to colored graphs, allowing for non-standard decompositions. We show that, given a suitable decomposition functor, the graph isomorphism problem reduces to checking isomorphism of colored prime graphs. Third, we extend the techniques of bounded color valence and hypergraph isomorphism on hypergraphs of bounded color class size as follows. We say a colored graph has generalized color valence at most k if, after removing all vertices in color classes of size at most k, for each color class C every vertex has at most k neighbors in C or at most k non-neighbors in C. We show that isomorphism of graphs of bounded generalized color valence can be solved in polynomial time.
Cite as
Pascal Schweitzer. Towards an Isomorphism Dichotomy for Hereditary Graph Classes. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 689-702, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{schweitzer:LIPIcs.STACS.2015.689,
author = {Schweitzer, Pascal},
title = {{Towards an Isomorphism Dichotomy for Hereditary Graph Classes}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {689--702},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.689},
URN = {urn:nbn:de:0030-drops-49513},
doi = {10.4230/LIPIcs.STACS.2015.689},
annote = {Keywords: graph isomorphism, modular decomposition, bounded color valence, reductions, forbidden induced subgraphs}
}
Document
Existential Second-order Logic over Graphs: A Complete Complexity-theoretic Classification
Abstract
Descriptive complexity theory aims at inferring a problem's computational complexity from the syntactic complexity of its description. A cornerstone of this theory is Fagin's Theorem, by which a property is expressible in existential second-order logic (ESO logic) if, and only if, it is in NP. A natural question, from the theory's point of view, is which syntactic fragments of ESO logic also still characterize NP. Research on this question has culminated in a dichotomy result by Gottlob, Kolaitis, and Schwentick: for each possible quantifier prefix of an ESO formula, the resulting prefix class over graphs either contains an NP-complete problem or is contained in P. However, the exact complexity of the prefix classes inside P remained elusive. In the present paper, we clear up the picture by showing that for each prefix class of ESO logic, its reduction closure under first-order reductions is either FO, L, NL, or NP. For undirected self-loop-free graphs two containment results are especially challenging to prove: containment in L for the prefix \exists R_1\cdots \exists R_n \forall x \exists y and containment in FO for the prefix \exists M \forall x \exists y for monadic M. The complex argument by Gottlob et al. concerning polynomial time needs to be carefully reexamined and either combined with the logspace version of Courcelle's Theorem or directly improved to first-order computations. A different challenge is posed by formulas with the prefix \exists M \forall x\forall y, which we show to express special constraint satisfaction problems that lie in L.
Cite as
Till Tantau. Existential Second-order Logic over Graphs: A Complete Complexity-theoretic Classification. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 703-715, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{tantau:LIPIcs.STACS.2015.703,
author = {Tantau, Till},
title = {{Existential Second-order Logic over Graphs: A Complete Complexity-theoretic Classification}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {703--715},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.703},
URN = {urn:nbn:de:0030-drops-49524},
doi = {10.4230/LIPIcs.STACS.2015.703},
annote = {Keywords: existential second-order logic, descriptive complexity, logarithmic space}
}
Document
The Returning Secretary
Abstract
In the online random-arrival model, an algorithm receives a sequence of $n$ requests that arrive in a random order. The algorithm is expected to make an irrevocable decision with regard to each request based only on the observed history. We consider the following natural extension of this model: each request arrives k times, and the arrival order is a random permutation of the kn arrivals; the algorithm is expected to make a decision regarding each request only upon its last arrival. We focus primarily on the case when k=2, which can also be interpreted as each request arriving at, and departing from the system, at a random time.
We examine the secretary problem: the problem of selecting the best secretary when the secretaries are presented online according to a random permutation. We show that when each secretary arrives twice, we can achieve a competitive ratio of 0.767974... (compared to 1/e in the classical secretary problem), and that it is optimal. We also show that without any knowledge about the number of secretaries or their arrival times, we can still hire the best secretary with probability at least 2/3, in contrast to the impossibility of achieving a constant success probability in the classical setting.
We extend our results to the matroid secretary problem, introduced by Babaioff et al. [3], and show a simple algorithm that achieves a 2-approximation to the maximal weighted basis in the new model (for k=2). We show that this approximation factor can be improved in special cases of the matroid secretary problem; in particular, we give a 16/9-competitive algorithm for the returning edge-weighted bipartite matching problem.
Cite as
Shai Vardi. The Returning Secretary. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 716-729, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{vardi:LIPIcs.STACS.2015.716,
author = {Vardi, Shai},
title = {{The Returning Secretary}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {716--729},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.716},
URN = {urn:nbn:de:0030-drops-49539},
doi = {10.4230/LIPIcs.STACS.2015.716},
annote = {Keywords: online algorithms, secretary problem, matroid secretary}
}
Document
Homomorphism Reconfiguration via Homotopy
Abstract
We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed into the other by changing one color at a time, maintaining an H-coloring throughout.This is the same as finding a path in the Hom(G,H) complex. For H=K_k this is the problem of finding paths between k-colorings, which was recently shown to be in P for k\leq 3 and PSPACE-complete otherwise (Bonsma and Cereceda 2009, Cereceda et al. 2011).
We generalize the positive side of this dichotomy by providing an algorithm that solves the problem in polynomial time for any H with no C_4 subgraph. This gives a large class of constraints for which finding solutions to the Constraint Satisfaction Problem is NP-complete, but paths in the solution space can be found in polynomial time.
The algorithm uses a characterization of possible reconfiguration sequences (that is, paths in Hom(G,H)), whose main part is a purely topological condition described in terms of the fundamental groupoid of H seen as a topological space.
Cite as
Marcin Wrochna. Homomorphism Reconfiguration via Homotopy. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 730-742, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{wrochna:LIPIcs.STACS.2015.730,
author = {Wrochna, Marcin},
title = {{Homomorphism Reconfiguration via Homotopy}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {730--742},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.730},
URN = {urn:nbn:de:0030-drops-49546},
doi = {10.4230/LIPIcs.STACS.2015.730},
annote = {Keywords: reconfiguration, recoloring, homomorphisms, homotopy, hom complex}
}
Document
Computing Downward Closures for Stacked Counter Automata
Abstract
The downward closure of a language L of words is the set of all (not necessarily contiguous) subwords of members of L. It is well known that the downward closure of any language is regular. Although the downward closure seems to be a promising abstraction, there are only few language classes for which an automaton for the downward closure is known to be computable. It is shown here that for stacked counter automata, the downward closure is computable. Stacked counter automata are finite automata with a storage mechanism obtained by adding blind counters and building stacks. Hence, they generalize pushdown and blind counter automata. The class of languages accepted by these automata are precisely those in the hierarchy obtained from the context-free languages by alternating two closure operators: imposing semilinear constraints and taking the algebraic extension. The main tool for computing downward closures is the new concept of Parikh annotations. As a second application of Parikh annotations, it is shown that the hierarchy above is strict at every level.
Cite as
Georg Zetzsche. Computing Downward Closures for Stacked Counter Automata. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 743-756, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
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@InProceedings{zetzsche:LIPIcs.STACS.2015.743,
author = {Zetzsche, Georg},
title = {{Computing Downward Closures for Stacked Counter Automata}},
booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages = {743--756},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-78-1},
ISSN = {1868-8969},
year = {2015},
volume = {30},
editor = {Mayr, Ernst W. and Ollinger, Nicolas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.743},
URN = {urn:nbn:de:0030-drops-49554},
doi = {10.4230/LIPIcs.STACS.2015.743},
annote = {Keywords: abstraction, downward closure, obstruction set, computability}
}