Volume
LIPIcs, Volume 20
30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
Event
STACS 2013, February 27 to March 2, 2013, Kiel, GermanyEditors
Publication Details
- published at: 2013-02-26
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-939897-50-7
- DBLP: db/conf/stacs/stacs2013
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Document
Complete Volume
LIPIcs, Volume 20, STACS'13, Complete Volume
Abstract
LIPIcs, Volume 20, STACS'13, Complete Volume
Cite as
30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@Proceedings{portier_et_al:LIPIcs.STACS.2013,
title = {{LIPIcs, Volume 20, STACS'13, Complete Volume}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013},
URN = {urn:nbn:de:0030-drops-41144},
doi = {10.4230/LIPIcs.STACS.2013},
annote = {Keywords: Models of Computation, Nonnumerical Algorithms and Problems, Mathematical Logic, Formal Languages, Combinatorics, Graph Theory}
}
Document
Front Matter
Frontmatter, Table of Contents, Preface, Workshop Organization
Abstract
Frontmatter, Table of Contents, Preface, Workshop Organization
Cite as
30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. i-xvii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{portier_et_al:LIPIcs.STACS.2013.i,
author = {Portier, Natacha and Wilke, Thomas},
title = {{Frontmatter, Table of Contents, Preface, Workshop Organization}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {i--xvii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.i},
URN = {urn:nbn:de:0030-drops-39135},
doi = {10.4230/LIPIcs.STACS.2013.i},
annote = {Keywords: Frontmatter, Table of Contents, Preface, Workshop Organization}
}
Document
Invited Talk
The complexity of analyzing infinite-state Markov chains, Markov decision processes, and stochastic games (Invited Talk)
Abstract
In recent years, a considerable amount of research has been devoted to understanding the computational complexity of basic analysis problems, and model checking problems, for finitely-presented countable infinite-state probabilistic systems. In particular, we have studied recursive Markov chains (RMCs), recursive Markov decision processes (RMDPs) and recursive stochastic games (RSGs). These arise by adding a natural recursion feature to finite-state Markov chains, MDPs, and stochastic games. RMCs and RMDPs provide natural abstract models of probabilistic procedural programs with recursion, and they are expressively equivalent to probabilistic and MDP extensions of pushdown automata. Moreover, a number of well-studied stochastic processes, including multi-type branching processes, (discrete-time) quasi-birth-death processes, and stochastic context-free grammars, can be suitably captured by subclasses of RMCs.
A central computational problem for analyzing various classes of recursive probabilistic systems is the computation of their (optimal) termination probabilities. These form a key ingredient for many other analyses, including model checking. For RMCs, and for important subclasses of RMDPs and RSGs, computing their termination values is equivalent to computing the least fixed point (LFP) solution of a corresponding monotone system of polynomial (min/max) equations. The complexity of computing the LFP solution for such equation systems is a intriguing problem, with connections to several areas of research. The LFP solution may in general be irrational. So, one possible aim is to compute it to within a desired additive error epsilon > 0. For general RMCs, approximating their termination probability within any non-trivial constant additive error < 1/2, is at least as hard as long-standing open problems in the complexity of numerical computation which are not even known to be in NP. For several key subclasses of RMCs and RMDPs, computing their termination values
turns out to be much more tractable.
In this talk I will survey algorithms for, and discuss the computational complexity of, key analysis problems for classes of infinite-state recursive MCs, MDPs, and stochastic games. In particular, I will discuss recent joint work with Alistair Stewart and Mihalis Yannakakis (in papers that appeared at STOC'12 and ICALP'12), in which we have obtained polynomial time algorithms for computing, to within arbitrary desired precision, the LFP solution of probabilistic polynomial (min/max) systems of equations. Using this, we obtained the first P-time algorithms for computing (within desired precision) the extinction probabilities of multi-type branching processes, the probability that an arbitrary given stochastic context-free grammar generates a given string, and the optimum (maximum or minimum) extinction probabilities for branching MDPs and context-free MDPs. For branching MDPs, their corresponding equations amount to Bellman optimality equations for minimizing/maximizing their termination probabilities. Our algorithms combine variations and generalizations of Newton's method with other techniques, including linear programming. The algorithms are fairly easy to implement, but analyzing their worst-case running time
is mathematically quite involved.
Cite as
Kousha Etessami. The complexity of analyzing infinite-state Markov chains, Markov decision processes, and stochastic games (Invited Talk). In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{etessami:LIPIcs.STACS.2013.1,
author = {Etessami, Kousha},
title = {{The complexity of analyzing infinite-state Markov chains, Markov decision processes, and stochastic games}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {1--2},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.1},
URN = {urn:nbn:de:0030-drops-39143},
doi = {10.4230/LIPIcs.STACS.2013.1},
annote = {Keywords: recursive Markov chains, Markov decision processes, stochastic games, monotone systems of nonlinear equations, least fixed points, Newton's method, co}
}
Document
Invited Talk
Graph coloring, communication complexity and the stubborn problem (Invited Talk)
Abstract
We discuss three equivalent forms of the same problem arising in communication complexity, constraint satisfaction problems, and graph coloring. Some partial results are discussed.
Cite as
Nicolas Bousquet, Aurélie Lagoutte, and Thomassé Stéphan. Graph coloring, communication complexity and the stubborn problem (Invited Talk). In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 3-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{bousquet_et_al:LIPIcs.STACS.2013.3,
author = {Bousquet, Nicolas and Lagoutte, Aur\'{e}lie and St\'{e}phan, Thomass\'{e}},
title = {{Graph coloring, communication complexity and the stubborn problem}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {3--4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.3},
URN = {urn:nbn:de:0030-drops-39158},
doi = {10.4230/LIPIcs.STACS.2013.3},
annote = {Keywords: stubborn problem, graph coloring, Clique-Stable set separation, Alon-Saks-Seymour conjecture, bipartite packing}
}
Document
Invited Talk
Physarum Computations (Invited Talk)
Abstract
Physarum is a slime mold. It was observed over the past 10 years that the mold is able to solve shortest path problems and to construct good Steiner networks [9, 11, 8].In a nutshell, the shortest path experiment is as follows: A maze is covered with mold and food is then provided at two positions s and t and the evolution of the slime is observed. Over time, the slime retracts to the shortest s-t-path. A video showing the wet-lab experiment can be found at
http://www.youtube.com/watch?v=tLO2n3YMcXw&t=4m43s. We strongly recommend to watch this video.
A mathematical model of the slime's dynamic behavior was proposed in 2007 [10]. Extensive computer simulations of the mathematical model confirm the wet-lab findings. For the edges on the shortest path, the diameter
converges to one, and for the edges off the shortest path, the diameter converges to zero.
We review the wet-lab and the computer experiments and provide a proof for these experimental findings. The proof was developed over a sequence of papers [6, 7, 4, 2, 1, 3]. We recommend the last two papers for first reading.
An interesting connection between Physarum and ant computations is made in [5].
Cite as
Kurt Mehlhorn. Physarum Computations (Invited Talk). In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 5-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{mehlhorn:LIPIcs.STACS.2013.5,
author = {Mehlhorn, Kurt},
title = {{Physarum Computations}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {5--6},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.5},
URN = {urn:nbn:de:0030-drops-39166},
doi = {10.4230/LIPIcs.STACS.2013.5},
annote = {Keywords: Biological computation, shortest path problems}
}
Document
Tutorial
Algorithmic Graph Structure Theory (Tutorial)
Abstract
The Graph Minors project of Robertson and Seymour uncovered a very deep structural theory of graphs. This theory had several important consequences, among others, the proof of Wagner's Conjecture. While the whole theory, presented in a series of 23 very dense papers, is notoriously difficult to understand, it has to be emphasized that these papers introduced several elementary concepts and tools that had strong impact on algorithms, complexity, and combinatorics. Moreover, even some of the very deep results can be stated in a compact and useful way, and it is possible to build upon these results without a complete understanding of the underlying machinery.
In the first part of the lecture, I will introduce the concept of treewidth, which can be thought of as an elementary entry point to graph minors theory. I will overview its graph-theoretic and algorithmic properties that make it especially important in the design of parameterized algorithms and approximation schemes on planar graphs. Furthermore, I will briefly explain some of the connections of treewidth to complexity and automata theory.
In the next part of the lecture, we will turn our attention to the more advanced topic of graphs excluding a fixed minor: the structure of such graphs, finding minors, and the well-quasi-ordering of the minor relation. The primary goal here is to provide clear and useful statements of these results and to show how they generalize the concepts of treewidth and planar graphs. Finally, I will briefly overview some more recent results involving different kinds of excluded structures, such as graphs excluding odd minors and topological minors.
Cite as
Dániel Marx. Algorithmic Graph Structure Theory (Tutorial). In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, p. 7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{marx:LIPIcs.STACS.2013.7,
author = {Marx, D\'{a}niel},
title = {{Algorithmic Graph Structure Theory}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {7--7},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.7},
URN = {urn:nbn:de:0030-drops-39175},
doi = {10.4230/LIPIcs.STACS.2013.7},
annote = {Keywords: Graph theory, graph minors, structure theorems}
}
Document
Searching for better fill-in
Abstract
Minimum Fill-in is a fundamental and classical problem arising in sparse matrix computations. In terms of graphs it can be formulated as a problem of finding a triangulation of a given graph with the minimum number of edges. By the classical result of Rose, Tarjan, Lueker, and Ohtsuki from 1976, an inclusion minimal triangulation of a graph can be found in polynomial time but, as it was shown by Yannakakis in 1981, finding a triangulation with the minimum number of edges is NP-hard.
In this paper, we study the parameterized complexity of local search for the Minimum Fill-in problem in the following form: Given a triangulation H of a graph G, is there a better triangulation, i.e. triangulation with less edges than H, within a given distance from H? We prove that this problem is fixed-parameter tractable (FPT) being parameterized by the distance from the initial triangulation by providing an algorithm that in time O(f(k) |G|^{O(1)}) decides if a better triangulation of G can be obtained by swapping at most k edges of H.
Our result adds Minimum Fill-in to the list of very few problems for which local search is known to be FPT.
Cite as
Fedor V. Fomin and Yngve Villanger. Searching for better fill-in. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 8-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{fomin_et_al:LIPIcs.STACS.2013.8,
author = {Fomin, Fedor V. and Villanger, Yngve},
title = {{Searching for better fill-in}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {8--19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.8},
URN = {urn:nbn:de:0030-drops-39187},
doi = {10.4230/LIPIcs.STACS.2013.8},
annote = {Keywords: Local Search, Parameterized Complexity, Fill-in, Triangulation, Chordal graph}
}
Document
Probably Optimal Graph Motifs
Abstract
We show an O^*(2^k)-time polynomial space algorithm for the k-sized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, Min-Substitute, and Min-Add.
Moreover, we provide a piece of evidence that our result might be essentially tight: the existence of an O^*((2-epsilon)^k)-time algorithm for the Graph Motif problem implies an ((2-epsilon')^n)-time algorithm for Set Cover.
Cite as
Andreas Björklund, Petteri Kaski, and Lukasz Kowalik. Probably Optimal Graph Motifs. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 20-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{bjorklund_et_al:LIPIcs.STACS.2013.20,
author = {Bj\"{o}rklund, Andreas and Kaski, Petteri and Kowalik, Lukasz},
title = {{Probably Optimal Graph Motifs}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {20--31},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.20},
URN = {urn:nbn:de:0030-drops-39196},
doi = {10.4230/LIPIcs.STACS.2013.20},
annote = {Keywords: graph motif, FPT algorithm}
}
Document
Tight bounds for Parameterized Complexity of Cluster Editing
Abstract
In the Correlation Clustering problem, also known as Cluster Editing, we are given an undirected graph G and a positive integer k; the task is to decide whether G can be transformed into a cluster graph, i.e., a disjoint union of cliques, by changing at most k adjacencies, that is, by adding or deleting at most k edges. The motivation of the problem stems from various tasks in computational biology (Ben-Dor et al., Journal of Computational Biology 1999) and machine learning (Bansal et al., Machine Learning 2004). Although in general Correlation Clustering is APX-hard (Charikar et al., FOCS 2003), the version of the problem where the number of cliques may not exceed a prescribed constant p admits a PTAS (Giotis and Guruswami, SODA 2006).
We study the parameterized complexity of Correlation Clustering with this restriction on the number of cliques to be created. We give an algorithm that - in time O(2^{O(sqrt{pk})} + n+m) decides whether a graph G on n vertices and m edges can be transformed into a cluster graph with exactly p cliques by changing at most k adjacencies.
We complement these algorithmic findings by the following, surprisingly tight lower bound on the asymptotic behavior of our algorithm. We show that unless the Exponential Time Hypothesis (ETH) fails - for any constant 0 <= sigma <= 1, there is p = Theta(k^sigma) such that there is no algorithm deciding in time 2^{o(sqrt{pk})} n^{O(1)} whether an n-vertex graph G can be transformed into a cluster graph with at most p cliques by changing at most k adjacencies.
Thus, our upper and lower bounds provide an asymptotically tight analysis of the multivariate parameterized complexity of the problem for the whole range of values of p from constant to a linear function of k.
Cite as
Fedor V. Fomin, Stefan Kratsch, Marcin Pilipczuk, Michal Pilipczuk, and Yngve Villanger. Tight bounds for Parameterized Complexity of Cluster Editing. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 32-43, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{fomin_et_al:LIPIcs.STACS.2013.32,
author = {Fomin, Fedor V. and Kratsch, Stefan and Pilipczuk, Marcin and Pilipczuk, Michal and Villanger, Yngve},
title = {{Tight bounds for Parameterized Complexity of Cluster Editing}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {32--43},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.32},
URN = {urn:nbn:de:0030-drops-39209},
doi = {10.4230/LIPIcs.STACS.2013.32},
annote = {Keywords: parameterized complexity, cluster editing, correlation clustering, subexponential algorithms, tight bounds}
}
Document
Bounded-width QBF is PSPACE-complete
Abstract
Tree-width is a well-studied parameter of structures that measures their similarity to a tree. Many important NP-complete problems, such as Boolean satisfiability (SAT), are tractable on bounded tree-width instances. In this paper we focus on the canonical PSPACE-complete problem QBF, the fully-quantified version of SAT. It was shown by Pan and Vardi [LICS 2006] that this problem is PSPACE-complete even for formulas whose tree-width grows extremely slowly. Vardi also posed the question of whether the problem is tractable when restricted to instances of bounded tree-width. We answer this question by showing that QBF on instances with constant tree-width is PSPACE-complete.
Cite as
Albert Atserias and Sergi Oliva. Bounded-width QBF is PSPACE-complete. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 44-54, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{atserias_et_al:LIPIcs.STACS.2013.44,
author = {Atserias, Albert and Oliva, Sergi},
title = {{Bounded-width QBF is PSPACE-complete}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {44--54},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.44},
URN = {urn:nbn:de:0030-drops-39217},
doi = {10.4230/LIPIcs.STACS.2013.44},
annote = {Keywords: Tree-width, QBF, PSPACE-complete}
}
Document
Model Counting for CNF Formulas of Bounded Modular Treewidth
Abstract
The modular treewidth of a graph is its treewidth after the contraction of modules. Modular treewidth properly generalizes treewidth and is itself properly generalized by clique-width. We show that the number of satisfying assignments of a CNF formula whose incidence graph has bounded modular treewidth can be computed in polynomial time. This provides new tractable classes of formulas for which #SAT is polynomial. In particular, our result generalizes known results for the treewidth of incidence graphs and is incomparable with known results for clique-width (or rank-width) of signed incidence graphs. The contraction of modules is an effective data reduction procedure. Our algorithm is the first one to harness this technique for #SAT. The order of the polynomial time bound of our algorithm depends on the modular treewidth. We show that this dependency cannot be avoided subject to an assumption from Parameterized Complexity.
Cite as
Daniel Paulusma, Friedrich Slivovsky, and Stefan Szeider. Model Counting for CNF Formulas of Bounded Modular Treewidth. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 55-66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{paulusma_et_al:LIPIcs.STACS.2013.55,
author = {Paulusma, Daniel and Slivovsky, Friedrich and Szeider, Stefan},
title = {{Model Counting for CNF Formulas of Bounded Modular Treewidth}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {55--66},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.55},
URN = {urn:nbn:de:0030-drops-39226},
doi = {10.4230/LIPIcs.STACS.2013.55},
annote = {Keywords: Satisfiability, Model Counting, Parameterized Complexity}
}
Document
Backdoors to q-Horn
Abstract
The class q-Horn, introduced by Boros, Crama and Hammer in 1990, is one of the largest known classes of propositional CNF formulas for which satisfiability can be decided in polynomial time. This class properly contains the fundamental classes of Horn and Krom formulas as well as the class of renamable (or disguised) Horn formulas.
In this paper we extend this class so that its favorable algorithmic properties can be made accessible to formulas that are outside but "close"' to this class. We show that deciding satisfiability is fixed-parameter tractable parameterized by the distance of the given formula from q-Horn. The distance is measured by the smallest number of variables that we need to delete from the formula in order to get a q-Horn formula, i.e., the size of a smallest deletion backdoor set into the class q-Horn.
This result generalizes known fixed-parameter tractability results for satisfiability decision with respect to the parameters distance from Horn, Krom, and renamable Horn.
Cite as
Serge Gaspers, Sebastian Ordyniak, M. S. Ramanujan, Saket Saurabh, and Stefan Szeider. Backdoors to q-Horn. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 67-79, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{gaspers_et_al:LIPIcs.STACS.2013.67,
author = {Gaspers, Serge and Ordyniak, Sebastian and Ramanujan, M. S. and Saurabh, Saket and Szeider, Stefan},
title = {{Backdoors to q-Horn}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {67--79},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.67},
URN = {urn:nbn:de:0030-drops-39236},
doi = {10.4230/LIPIcs.STACS.2013.67},
annote = {Keywords: Algorithms and data structures, Backdoor sets, Satisfiability, Fixed Parameter Tractability}
}
Document
On Polynomial Kernels for Sparse Integer Linear Programs
Abstract
Integer linear programs (ILPs) are a widely applied framework for dealing with combinatorial problems that arise in practice. It is known, e.g., by the success of CPLEX, that preprocessing and simplification can greatly speed up the process of optimizing an ILP. The present work seeks to further the theoretical understanding of preprocessing for ILPs by initiating a rigorous study within the framework of parameterized complexity and kernelization.
A famous result of Lenstra (Mathematics of Operations Research, 1983) shows that feasibility of any ILP with n variables and m constraints can be decided in time O(c^{n^3} m^{c'}). Thus, by a folklore argument, any such ILP admits a kernelization to an equivalent instance of size O(c^{n^3}). It is known, that unless \containment and the polynomial hierarchy collapses, no kernelization with size bound polynomial in n is possible. However, this lower bound only applies for the case when constraints may include an arbitrary number of variables since it follows from lower bounds for \sat and \hittingset, whose bounded arity variants admit polynomial kernelizations.
We consider the feasibility problem for ILPs Ax <= b where A is an r-row-sparse matrix parameterized by the number of variables. We show that the kernelizability of this problem depends strongly on the range of the variables. If the range is unbounded then this problem does not admit a polynomial kernelization unless \containment. If, on the other hand, the range of each variable is polynomially bounded in n then we do get a polynomial kernelization. Additionally, this holds also for the more general case when the maximum range d is an additional parameter, i.e., the size obtained is polynomial in n+d.
Cite as
Stefan Kratsch. On Polynomial Kernels for Sparse Integer Linear Programs. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 80-91, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{kratsch:LIPIcs.STACS.2013.80,
author = {Kratsch, Stefan},
title = {{On Polynomial Kernels for Sparse Integer Linear Programs}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {80--91},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.80},
URN = {urn:nbn:de:0030-drops-39241},
doi = {10.4230/LIPIcs.STACS.2013.80},
annote = {Keywords: integer linear programs, kernelization, parameterized complexity}
}
Document
Linear kernels for (connected) dominating set on graphs with excluded topological subgraphs
Abstract
We give the first linear kernels for Dominating Set and Connected Dominating Set problems on graphs excluding a fixed graph H as a topological minor.
Cite as
Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, and Dimitrios M. Thilikos. Linear kernels for (connected) dominating set on graphs with excluded topological subgraphs. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 92-103, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{fomin_et_al:LIPIcs.STACS.2013.92,
author = {Fomin, Fedor V. and Lokshtanov, Daniel and Saurabh, Saket and Thilikos, Dimitrios M.},
title = {{Linear kernels for (connected) dominating set on graphs with excluded topological subgraphs}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {92--103},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.92},
URN = {urn:nbn:de:0030-drops-39255},
doi = {10.4230/LIPIcs.STACS.2013.92},
annote = {Keywords: Parameterized complexity, kernelization, algorithmic graph minors, dominating set, connected dominating set}
}
Document
The PCP theorem for NP over the reals
Abstract
In this paper we show that the PCP theorem holds as well in the real
number computational model introduced by Blum, Shub, and Smale.
More precisely, the real number counterpart NP_R of the classical
Turing model class NP can be characterized as NP_R = PCP_R(O(log n), O(1)). Our proof structurally follows the one by Dinur for classical NP. However, a lot of minor and major changes are necessary due to the real numbers as underlying computational structure. The analogue result holds for the complex numbers and NP_C.
Cite as
Martijn Baartse and Klaus Meer. The PCP theorem for NP over the reals. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 104-115, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{baartse_et_al:LIPIcs.STACS.2013.104,
author = {Baartse, Martijn and Meer, Klaus},
title = {{The PCP theorem for NP over the reals}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {104--115},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.104},
URN = {urn:nbn:de:0030-drops-39262},
doi = {10.4230/LIPIcs.STACS.2013.104},
annote = {Keywords: PCP, real number computation, systems of polynomials}
}
Document
Mutual Dimension
Abstract
We define the lower and upper mutual dimensions mdim(x:y) and Mdim(x:y) between any two points x and y in Euclidean space. Intuitively these are the lower and upper densities of the algorithmic information shared by x and y. We show that these quantities satisfy the main desiderata for a satisfactory measure of mutual algorithmic information. Our main theorem, the data processing inequality for mutual dimension, says that, if f : R^m -> R^n is computable and Lipschitz, then the inequalities mdim(f(x):y) <= mdim(x:y) and Mdim(f(x):y) <= Mdim(x:y) hold for all x \in R^m and y \in R^t. We use this inequality and related inequalities that we prove in like fashion to establish conditions under which various classes of computable functions on Euclidean space preserve or otherwise transform mutual dimensions between points.
Cite as
Adam Case and Jack H. Lutz. Mutual Dimension. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 116-126, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{case_et_al:LIPIcs.STACS.2013.116,
author = {Case, Adam and Lutz, Jack H.},
title = {{Mutual Dimension}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {116--126},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.116},
URN = {urn:nbn:de:0030-drops-39270},
doi = {10.4230/LIPIcs.STACS.2013.116},
annote = {Keywords: computable analysis, data processing inequality, effective fractal dimensions, Kolmogorov complexity, mutual information}
}
Document
Exact and Approximation Algorithms for the Maximum Constraint Satisfaction Problem over the Point Algebra
Abstract
We study the constraint satisfaction problem over the point algebra.
In this problem, an instance consists of a set of variables and a set of binary constraints of forms (x < y), (x <= y), (x \neq y) or (x = y). Then, the objective is to assign integers to variables so as to satisfy as many constraints as possible.This problem contains many important problems such as Correlation Clustering, Maximum Acyclic Subgraph, and Feedback Arc Set.
We first give an exact algorithm that runs in O^*(3^{\frac{log 5}{log 6}n}) time, which improves the previous best O^*(3^n) obtained by a standard dynamic programming.
Our algorithm combines the dynamic programming with the split-and-list technique. The split-and-list technique involves matrix products and we make use of sparsity of matrices to speed up the computation.
As for approximation, we give a 0.4586-approximation algorithm when the objective is maximizing the number of satisfied constraints, and give an O(log n log log n)-approximation algorithm when the objective is minimizing the number of unsatisfied constraints.
Cite as
Yoichi Iwata and Yuichi Yoshida. Exact and Approximation Algorithms for the Maximum Constraint Satisfaction Problem over the Point Algebra. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 127-138, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{iwata_et_al:LIPIcs.STACS.2013.127,
author = {Iwata, Yoichi and Yoshida, Yuichi},
title = {{Exact and Approximation Algorithms for the Maximum Constraint Satisfaction Problem over the Point Algebra}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {127--138},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.127},
URN = {urn:nbn:de:0030-drops-39282},
doi = {10.4230/LIPIcs.STACS.2013.127},
annote = {Keywords: Constraint Satisfaction Problems, Point Algebra, Exact Algorithms, Approximation Algorithms}
}
Document
Local Search is Better than Random Assignment for Bounded Occurrence Ordering k-CSPs
Abstract
We prove that the Bounded Occurrence Ordering k-CSP Problem is not approximation resistant. We give a very simple local search algorithm that always performs better than the random assignment algorithm (unless, the number of satisfied constraints does not depend on the ordering). Specifically, the expected value of the solution returned by the algorithm is at least ALG >= AVG + alpha(B,k)(OPT-AVG), where OPT is the value of the optimal solution; AVG is the expected value of the random solution; and alpha(B,k) = Omega_k(B^{-(k+O(1))}) is a parameter depending only on k (the arity of the CSP) and B (the maximum number of times each variable is used in constraints).
The question whether bounded occurrence ordering k-CSPs are approximation resistant was raised by Guruswami and Zhou (2012), who recently showed that bounded occurrence 3-CSPs and "monotone" k-CSPs admit a non-trivial approximation.
Cite as
Konstantin Makarychev. Local Search is Better than Random Assignment for Bounded Occurrence Ordering k-CSPs. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 139-147, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{makarychev:LIPIcs.STACS.2013.139,
author = {Makarychev, Konstantin},
title = {{Local Search is Better than Random Assignment for Bounded Occurrence Ordering k-CSPs}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {139--147},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.139},
URN = {urn:nbn:de:0030-drops-39290},
doi = {10.4230/LIPIcs.STACS.2013.139},
annote = {Keywords: approximation algorithms, approximation resistance, ordering CSPs}
}
Document
The complexity of approximating conservative counting CSPs
Abstract
We study the complexity of approximation for a weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, a classification is known for the Boolean domain. We give a classification for problems with general finite domain. We define weak log-modularity and weak log-supermodularity, and show that #CSP(F) is in FP if F is weakly log-modular. Otherwise, it is at least as hard to approximate as #BIS, counting independent sets in bipartite graphs, which is believed to be intractable. We further sub-divide the #BIS-hard case. If F is weakly log-supermodular, we show that #CSP(F) is as easy as Boolean log-supermodular weighted #CSP. Otherwise, it is NP-hard to approximate. Finally, we give a trichotomy for the arity-2 case.
Then, #CSP(F) is in FP, is #BIS-equivalent, or is equivalent to #SAT, the problem of approximately counting satisfying assignments of a CNF Boolean formula.
Cite as
Xi Chen, Martin Dyer, Leslie Ann Goldberg, Mark Jerrum, Pinyan Lu, Colin McQuillan, and David Richerby. The complexity of approximating conservative counting CSPs. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 148-159, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{chen_et_al:LIPIcs.STACS.2013.148,
author = {Chen, Xi and Dyer, Martin and Goldberg, Leslie Ann and Jerrum, Mark and Lu, Pinyan and McQuillan, Colin and Richerby, David},
title = {{The complexity of approximating conservative counting CSPs}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {148--159},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.148},
URN = {urn:nbn:de:0030-drops-39303},
doi = {10.4230/LIPIcs.STACS.2013.148},
annote = {Keywords: counting constraint satisfaction problem, approximation, complexity}
}
Document
Lossy Chains and Fractional Secret Sharing
Abstract
Motivated by the goal of controlling the amount of work required to access a shared resource or to solve a cryptographic puzzle, we introduce and study the related notions of lossy chains and fractional secret sharing.
Fractional secret sharing generalizes traditional secret sharing by allowing a fine-grained control over the amount of uncertainty about the secret. More concretely, a fractional secret sharing scheme realizes a fractional access structure f : 2^{[n]} -> {0,...,m-1} by guaranteeing that from the point of view of each set T \subseteq [n] of parties, the secret is uniformly distributed over a set of f(T) + 1 potential secrets. We show that every (monotone) fractional access structure can be realized. For symmetric structures, in which f(T) depends only on the size of T, we give an efficient construction with share size poly(n,log m).
Our construction of fractional secret sharing schemes is based on the new notion of lossy chains which may be of independent interest.
A lossy chain is a Markov chain (X_0,...,X_n) which starts with a random secret X_0 and gradually loses information about it at a rate which is specified by a loss function g. Concretely, in every step t, the distribution of X_0 conditioned on the value of X_t should always be uniformly distributed over a set of size g(t). We show how to construct such lossy chains efficiently for any possible loss function g, and prove that our construction achieves an optimal asymptotic information rate.
Cite as
Yuval Ishai, Eyal Kushilevitz, and Omer Strulovich. Lossy Chains and Fractional Secret Sharing. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 160-171, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{ishai_et_al:LIPIcs.STACS.2013.160,
author = {Ishai, Yuval and Kushilevitz, Eyal and Strulovich, Omer},
title = {{Lossy Chains and Fractional Secret Sharing}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {160--171},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.160},
URN = {urn:nbn:de:0030-drops-39319},
doi = {10.4230/LIPIcs.STACS.2013.160},
annote = {Keywords: Cryptography, secret sharing, Markov chains}
}
Document
Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM
Abstract
We study the difference between the standard seeded model (aTAM) of tile self-assembly, and the "seedless" two-handed model of tile self-assembly (2HAM). Most of our results suggest that the two-handed model is more powerful. In particular, we show how to simulate any seeded system with a two-handed system that is essentially just a constant factor larger. We exhibit finite shapes with a busy-beaver separation in the number of distinct tiles required by seeded versus two-handed, and exhibit an infinite shape that can be constructed two-handed but not seeded. Finally, we show that verifying whether a given system uniquely assembles a desired supertile is co-NP-complete in the two-handed model, while it was known to be polynomially solvable in the seeded model.
Cite as
Sarah Cannon, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Matthew J. Patitz, Robert T. Schweller, Scott M Summers, and Andrew Winslow. Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 172-184, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{cannon_et_al:LIPIcs.STACS.2013.172,
author = {Cannon, Sarah and Demaine, Erik D. and Demaine, Martin L. and Eisenstat, Sarah and Patitz, Matthew J. and Schweller, Robert T. and Summers, Scott M and Winslow, Andrew},
title = {{Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {172--184},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.172},
URN = {urn:nbn:de:0030-drops-39321},
doi = {10.4230/LIPIcs.STACS.2013.172},
annote = {Keywords: abstract tile assembly model, hierarchical tile assembly model, two-handed tile assembly model, algorithmic self-assembly, DNA computing, biocomputing}
}
Document
Unlabeled Data Does Provably Help
Abstract
A fully supervised learner needs access to correctly labeled examples whereas a semi-supervised learner has access to examples part of which are labeled and part of which are not. The hope is that a large collection of unlabeled examples significantly reduces the need for labeled-ones. It is widely believed that this reduction of "label complexity" is marginal unless the hidden target concept and the domain distribution satisfy some "compatibility assumptions". There are some recent papers in support of this belief. In this paper, we revitalize the discussion by presenting a result that goes in the other direction. To this end, we consider the PAC-learning model in two settings: the (classical) fully supervised setting and the semi-supervised setting. We show that the "label-complexity gap"' between the semi-supervised and the fully supervised setting can become arbitrarily large for concept classes of infinite VC-dimension (or sequences of classes whose VC-dimensions are finite but become arbitrarily large). On the other hand, this gap is bounded by O(ln |C|) for each finite concept class C that contains the constant zero- and the constant one-function. A similar statement holds for all classes C of finite VC-dimension.
Cite as
Malte Darnstädt, Hans Ulrich Simon, and Balázs Szörényi. Unlabeled Data Does Provably Help. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 185-196, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{darnstadt_et_al:LIPIcs.STACS.2013.185,
author = {Darnst\"{a}dt, Malte and Simon, Hans Ulrich and Sz\"{o}r\'{e}nyi, Bal\'{a}zs},
title = {{Unlabeled Data Does Provably Help}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {185--196},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.185},
URN = {urn:nbn:de:0030-drops-39337},
doi = {10.4230/LIPIcs.STACS.2013.185},
annote = {Keywords: algorithmic learning, sample complexity, semi-supervised learning}
}
Document
Computing cutwidth and pathwidth of semi-complete digraphs via degree orderings
Abstract
The notions of cutwidth and pathwidth of digraphs play a central role in the containment theory for tournaments, or more generally semi-complete digraphs, developed in a recent series of papers by Chudnovsky, Fradkin, Kim, Scott, and Seymour (Maria Chudnovsky, Alexandra Fradkin, and Paul Seymour, 2012; Maria Chudnovsky, Alex Scott, and Paul Seymour, 2011; Maria Chudnovsky and Paul D. Seymour, 2011; Alexandra Fradkin and Paul Seymour, 2010; Alexandra Fradkin and Paul Seymour, 2011; Ilhee Kim and Paul Seymour, 2012). In this work we introduce a new approach to computing these width measures on semi-complete digraphs, via degree orderings. Using the new technique we are able to reprove the main results of (Maria Chudnovsky, Alexandra Fradkin, and Paul Seymour, 2012; Alexandra Fradkin and Paul Seymour, 2011) in a unified and significantly simplified way, as well as obtain new results. First, we present polynomial-time approximation algorithms for both cutwidth and pathwidth, faster and simpler than the previously known ones; the most significant improvement is in case of pathwidth, where instead of previously known O(OPT)-approximation in fixed-parameter tractable time (Fedor V. Fomin and Michal Pilipczuk, 2013) we obtain a constant-factor approximation in polynomial time. Secondly, by exploiting the new set of obstacles for cutwidth and pathwidth, we show that topological containment and immersion in semi-complete digraphs can be tested in single-exponential fixed-parameter tractable time. Finally, we present how the new approach can be used to obtain exact fixed-parameter tractable algorithms for cutwidth and pathwidth, with single-exponential running time dependency on the optimal width.
Cite as
Michal Pilipczuk. Computing cutwidth and pathwidth of semi-complete digraphs via degree orderings. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 197-208, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{pilipczuk:LIPIcs.STACS.2013.197,
author = {Pilipczuk, Michal},
title = {{Computing cutwidth and pathwidth of semi-complete digraphs via degree orderings}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {197--208},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.197},
URN = {urn:nbn:de:0030-drops-39340},
doi = {10.4230/LIPIcs.STACS.2013.197},
annote = {Keywords: semi-complete digraph, tournament, pathwidth, cutwidth}
}
Document
On Pairwise Spanners
Abstract
Given an undirected n-node unweighted graph G = (V, E), a spanner with stretch function f(.) is a subgraph H \subseteq G such that, if two nodes are at distance d in G, then they are at distance at most f(d) in H. Spanners are very well studied in the literature. The typical goal is to construct the sparsest possible spanner for a given stretch function.
In this paper we study pairwise spanners, where we require to approximate the u-v distance only for pairs (u,v) in a given set P \subseteq V x V. Such P-spanners were studied before [Coppersmith,Elkin'05] only in the special case that f(.) is the identity function, i.e. distances between relevant pairs must be preserved exactly (a.k.a. pairwise preservers).
Here we present pairwise spanners which are at the same time sparser than the best known preservers (on the same P) and of the best known spanners (with the same f(.)).
In more detail, for arbitrary P, we show that there exists a P-spanner of size O(n(|P|log n)^{1/4}) with f(d) = d + 4 log n. Alternatively, for any epsislon > 0, there exists a P-spanner of size O(n|P|^{1/4} sqrt{(log n) / epsilon}) with f(d) = (1 + epsilon)d + 4. We also consider the relevant special case that there is a critical set of nodes S \subseteq V, and we wish to approximate either the distances within nodes in S or from nodes in S to any other node. We show that there exists an (S x S)-spanner of size O(n sqrt{|S|}) with f(d) = d + 2, and an (S x V)-spanner of size O(n sqrt{|S| log n}) with f(d) = d + 2 log n. All the mentioned pairwise spanners can be constructed in polynomial time.
Cite as
Marek Cygan, Fabrizio Grandoni, and Telikepalli Kavitha. On Pairwise Spanners. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 209-220, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{cygan_et_al:LIPIcs.STACS.2013.209,
author = {Cygan, Marek and Grandoni, Fabrizio and Kavitha, Telikepalli},
title = {{On Pairwise Spanners}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {209--220},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.209},
URN = {urn:nbn:de:0030-drops-39353},
doi = {10.4230/LIPIcs.STACS.2013.209},
annote = {Keywords: Undirected graphs, shortest paths, additive spanners, distance preservers}
}
Document
Excluded vertex-minors for graphs of linear rank-width at most k.
Abstract
Linear rank-width is a graph width parameter, which is a variation of rank-width by restricting its tree to a caterpillar. As a corollary of known theorems, for each k, there is a finite set \mathcal{O}_k of graphs such that a graph G has linear rank-width at most k if and only if no vertex-minor of G is isomorphic to a graph in \mathcal{O}_k. However, no attempts have been made to bound the number of graphs in \mathcal{O}_k for k >= 2. We construct, for each k, 2^{\Omega(3^k)} pairwise locally non-equivalent graphs that are excluded vertex-minors for graphs of linear rank-width at most k.
Therefore the number of graphs in \mathcal{O}_k is at least double exponential.
Cite as
Jisu Jeong, O-joung Kwon, and Sang-il Oum. Excluded vertex-minors for graphs of linear rank-width at most k.. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 221-232, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{jeong_et_al:LIPIcs.STACS.2013.221,
author = {Jeong, Jisu and Kwon, O-joung and Oum, Sang-il},
title = {{Excluded vertex-minors for graphs of linear rank-width at most k.}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {221--232},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.221},
URN = {urn:nbn:de:0030-drops-39369},
doi = {10.4230/LIPIcs.STACS.2013.221},
annote = {Keywords: rank-width, linear rank-width, vertex-minor, well-quasi-ordering}
}
Document
Recompression: a simple and powerful technique for word equations
Abstract
We present an application of a local recompression technique, previously developed by the author in the context of compressed membership problems and compressed pattern matching, to word equations. The technique is based on local modification of variables (replacing X by aX or Xa) and replacement of pairs of letters appearing in the equation by a 'fresh' letter, which can be seen as a bottom-up compression of the solution of the given word equation, to be more specific, building an SLP (Straight-Line Programme) for the solution of the word equation.
Using this technique we give new self-contained proofs of many known results for word equations: the presented nondeterministic algorithm runs in O(n log n) space and in time polynomial in log N and n, where N is the size of the length-minimal solution of the word equation.
It can be easily generalised to a generator of all solutions of the word equation. A further analysis of the algorithm yields a doubly exponential upper bound on the size of the length-minimal solution.
The presented algorithm does not use exponential bound on the exponent of periodicity. Conversely, the analysis of the algorithm yields a new proof of the exponential bound on exponent of periodicity. For O(1) variables with arbitrary many appearances it works in linear space.
Cite as
Artur Jez. Recompression: a simple and powerful technique for word equations. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 233-244, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{jez:LIPIcs.STACS.2013.233,
author = {Jez, Artur},
title = {{Recompression: a simple and powerful technique for word equations}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {233--244},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.233},
URN = {urn:nbn:de:0030-drops-39376},
doi = {10.4230/LIPIcs.STACS.2013.233},
annote = {Keywords: Word equations, exponent of periodicity, string unification}
}
Document
Fast Algorithms for Abelian Periods in Words and Greatest Common Divisor Queries
Abstract
We present efficient algorithms computing all Abelian periods of two types in a word. Regular Abelian periods are computed in O(n log log{n}) randomized time which improves over the best previously known algorithm by almost a factor of n. The other algorithm, for full Abelian periods, works in O(n) time. As a tool we develop an O(n) time construction of a data structure that allows O(1) time gcd(i,j) queries for all 1 <= i,j <= n, this is a result of independent interest.
Cite as
Tomasz Kociumaka, Jakub Radoszewski, and Wojciech Rytter. Fast Algorithms for Abelian Periods in Words and Greatest Common Divisor Queries. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 245-256, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{kociumaka_et_al:LIPIcs.STACS.2013.245,
author = {Kociumaka, Tomasz and Radoszewski, Jakub and Rytter, Wojciech},
title = {{Fast Algorithms for Abelian Periods in Words and Greatest Common Divisor Queries}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {245--256},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.245},
URN = {urn:nbn:de:0030-drops-39387},
doi = {10.4230/LIPIcs.STACS.2013.245},
annote = {Keywords: Abelian period, greatest common divisor}
}
Document
Finding Pseudo-repetitions
Abstract
Pseudo-repetitions are a natural generalization of the classical notion of repetitions in sequences. We solve fundamental algorithmic questions on pseudo-repetitions by application of insightful combinatorial results on words. More precisely, we efficiently decide whether a word is a pseudo-repetition and find all the pseudo-repetitive factors of a word.
Cite as
Pawel Gawrychowski, Florin Manea, Robert Mercas, Dirk Nowotka, and Catalin Tiseanu. Finding Pseudo-repetitions. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 257-268, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{gawrychowski_et_al:LIPIcs.STACS.2013.257,
author = {Gawrychowski, Pawel and Manea, Florin and Mercas, Robert and Nowotka, Dirk and Tiseanu, Catalin},
title = {{Finding Pseudo-repetitions}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {257--268},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.257},
URN = {urn:nbn:de:0030-drops-39394},
doi = {10.4230/LIPIcs.STACS.2013.257},
annote = {Keywords: Stringology, Pattern matching, Repetition, Pseudo-repetition}
}
Document
Algorithms for Designing Pop-Up Cards
Abstract
We prove that every simple polygon can be made as a (2D) pop-up card/book that opens to any desired angle between 0 and 360°.
More precisely, given a simple polygon attached to the two walls of the open pop-up, our polynomial-time algorithm subdivides the polygon into a single-degree-of-freedom linkage structure, such that closing the pop-up flattens the linkage without collision. This result solves an open problem of Hara and Sugihara from 2009. We also show how to obtain a more efficient construction for the special case of orthogonal polygons, and how to make 3D orthogonal polyhedra, from pop-ups that open to 90°, 180°, 270°, or 360°.
Cite as
Zachary Abel, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Anna Lubiw, André Schulz, Diane L. Souvaine, Giovanni Viglietta, and Andrew Winslow. Algorithms for Designing Pop-Up Cards. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 269-280, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{abel_et_al:LIPIcs.STACS.2013.269,
author = {Abel, Zachary and Demaine, Erik D. and Demaine, Martin L. and Eisenstat, Sarah and Lubiw, Anna and Schulz, Andr\'{e} and Souvaine, Diane L. and Viglietta, Giovanni and Winslow, Andrew},
title = {{Algorithms for Designing Pop-Up Cards}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {269--280},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.269},
URN = {urn:nbn:de:0030-drops-39407},
doi = {10.4230/LIPIcs.STACS.2013.269},
annote = {Keywords: geometric folding, linkages, universality}
}
Document
Space-Time Trade-offs for Stack-Based Algorithms
Abstract
In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space bottleneck is a stack into memory-constrained algorithms. Given an algorithm A that runs in O(n) time using a stack of length Theta(n), we can modify it so that it runs in O(n^2/2^s) time using a workspace of O(s) variables (for any s \in o(log n)) or O(n log n/log p)$ time using O(p log n/log p) variables (for any 2 <= p <= n). We also show how the technique can be applied to solve various geometric problems, namely computing the convex hull of a simple polygon, a triangulation of a monotone polygon, the shortest path between two points inside a monotone polygon, 1-dimensional pyramid approximation of a 1-dimensional vector, and the visibility profile of a point inside a simple polygon. Our approach exceeds or matches the best-known results for these problems in constant-workspace models (when they exist), and gives a trade-off between the size of the workspace and running time. To the best of our knowledge, this is the first general framework for obtaining memory-constrained algorithms.
Cite as
Luis Barba, Matias Korman, Stefan Langerman, Rodrigo I. Silveira, and Kunihiko Sadakane. Space-Time Trade-offs for Stack-Based Algorithms. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 281-292, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{barba_et_al:LIPIcs.STACS.2013.281,
author = {Barba, Luis and Korman, Matias and Langerman, Stefan and Silveira, Rodrigo I. and Sadakane, Kunihiko},
title = {{Space-Time Trade-offs for Stack-Based Algorithms}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {281--292},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.281},
URN = {urn:nbn:de:0030-drops-39411},
doi = {10.4230/LIPIcs.STACS.2013.281},
annote = {Keywords: space-time trade-off, constant workspace, stack algorithms}
}
Document
L_1 Shortest Path Queries among Polygonal Obstacles in the Plane
Abstract
Given a point s and a set of h pairwise disjoint polygonal obstacles with a total of n vertices in the plane, after the free space is triangulated, we present an O(n+h log h) time and O(n) space algorithm for building a data structure (called shortest path map) of size O(n) such that for any query point t, the length of the L_1 shortest obstacle-avoiding path from s to t can be reported in O(log n) time and the actual path can be found in additional time proportional to the number of edges of the path. Previously, the best algorithm computes such a shortest path map in O(n log n) time and O(n) space. In addition, our techniques also yield an improved algorithm for computing the L_1 geodesic Voronoi diagram of m point sites among the obstacles.
Cite as
Danny Z. Chen and Haitao Wang. L_1 Shortest Path Queries among Polygonal Obstacles in the Plane. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 293-304, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{chen_et_al:LIPIcs.STACS.2013.293,
author = {Chen, Danny Z. and Wang, Haitao},
title = {{L\underline1 Shortest Path Queries among Polygonal Obstacles in the Plane}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {293--304},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.293},
URN = {urn:nbn:de:0030-drops-39425},
doi = {10.4230/LIPIcs.STACS.2013.293},
annote = {Keywords: computational geometry, shortest path queries, shortest paths among obstacles, \$L\underline1\$/\$L\underlineinfty\$/rectilinear metric, shortest path maps, geodesic Vorono}
}
Document
Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable
Abstract
We consider the quantifier alternation hierarchy within two-variable first-order logic FO^2[<,suc] over finite words with linear order and binary successor predicate. We give a single identity of omega-terms for each level of this hierarchy. This shows that for a given regular language and a non-negative integer~$m$ it is decidable whether the language is definable by a formula in FO^2[<,suc] which has at most m quantifier alternations. We also consider the alternation hierarchy of unary temporal logic TL[X,F,Y,P] defined by the maximal number of nested negations. This hierarchy coincides with the FO^2[<,suc] quantifier alternation hierarchy.
Cite as
Manfred Kufleitner and Alexander Lauser. Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 305-316, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{kufleitner_et_al:LIPIcs.STACS.2013.305,
author = {Kufleitner, Manfred and Lauser, Alexander},
title = {{Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {305--316},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.305},
URN = {urn:nbn:de:0030-drops-39438},
doi = {10.4230/LIPIcs.STACS.2013.305},
annote = {Keywords: automata theory, semigroups, regular languages, first-order logic}
}
Document
FO^2 with one transitive relation is decidable
Abstract
We show that the satisfiability problem for the two-variable first-order logic, FO^2, over transitive structures when only one relation is required to be transitive, is decidable. The result is optimal, as FO^2 over structures with two transitive relations, or with one transitive and one equivalence relation, are known to be undecidable, so in fact, our result completes the classification of FO^2-logics over transitive structures with respect to decidability.
We show that the satisfiability problem is in 2-NExpTime.
Decidability of the finite satisfiability problem remains open.
Cite as
Wieslaw Szwast and Lidia Tendera. FO^2 with one transitive relation is decidable. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 317-328, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{szwast_et_al:LIPIcs.STACS.2013.317,
author = {Szwast, Wieslaw and Tendera, Lidia},
title = {{FO^2 with one transitive relation is decidable}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {317--328},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.317},
URN = {urn:nbn:de:0030-drops-39449},
doi = {10.4230/LIPIcs.STACS.2013.317},
annote = {Keywords: classical decision problem, two-variable first-order logic, decidability, computational complexity}
}
Document
Two-variable first order logic with modular predicates over words
Abstract
We consider first order formulae over the signature consisting of the symbols of the alphabet, the symbol < (interpreted as a linear order) and the set MOD of modular numerical predicates. We study the expressive power of FO^2[<,MOD], the two-variable first order logic over this signature, interpreted over finite words. We give an algebraic characterization of the corresponding regular languages in terms of their syntactic morphisms and we also give simple unambiguous regular expressions for them. It follows that one can decide whether a given regular language is captured by FO^2[<,MOD]. Our proofs rely on a combination of arguments from semigroup theory (stamps), model theory (Ehrenfeucht-Fraïssé games) and combinatorics.
Cite as
Luc Dartois and Charles Paperman. Two-variable first order logic with modular predicates over words. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 329-340, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{dartois_et_al:LIPIcs.STACS.2013.329,
author = {Dartois, Luc and Paperman, Charles},
title = {{Two-variable first order logic with modular predicates over words}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {329--340},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.329},
URN = {urn:nbn:de:0030-drops-39450},
doi = {10.4230/LIPIcs.STACS.2013.329},
annote = {Keywords: First order logic, automata theory, semigroup, modular predicates}
}
Document
Abusing the Tutte Matrix: An Algebraic Instance Compression for the K-set-cycle Problem
Abstract
We give an algebraic, determinant-based algorithm for the K-Cycle problem, i.e., the problem of finding a cycle through a set of specified elements. Our approach gives a simple FPT algorithm for the problem, matching the O^*(2^|K|) running time of the algorithm of Björklund et al. (SODA, 2012). Furthermore, our approach is open for treatment by classical algebraic tools (e.g., Gaussian elimination), and we show that it leads to a polynomial compression of the problem, i.e., a polynomial-time reduction of the K-Cycle problem into an algebraic problem with coding size O(|K|^3).
This is surprising, as several related problems (e.g., k-Cycle and the Disjoint Paths problem) are known not to admit such a reduction unless the polynomial hierarchy collapses. Furthermore, despite the result, we are not aware of any witness for the K-Cycle problem of size polynomial in |K|+ log n, which seems (for now) to separate the notions of polynomial compression and polynomial kernelization (as a polynomial kernelization for a problem in NP necessarily implies a small witness).
Cite as
Magnus Wahlström. Abusing the Tutte Matrix: An Algebraic Instance Compression for the K-set-cycle Problem. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 341-352, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{wahlstrom:LIPIcs.STACS.2013.341,
author = {Wahlstr\"{o}m, Magnus},
title = {{Abusing the Tutte Matrix: An Algebraic Instance Compression for the K-set-cycle Problem}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {341--352},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.341},
URN = {urn:nbn:de:0030-drops-39465},
doi = {10.4230/LIPIcs.STACS.2013.341},
annote = {Keywords: Parameterized complexity, graph theory, kernelization, algebraic algorithms}
}
Document
Subexponential-Time Parameterized Algorithm for Steiner Tree on Planar Graphs
Abstract
The well-known bidimensionality theory provides a method for designing fast, subexponential-time parameterized algorithms for a vast number of NP-hard problems on sparse graph classes such as planar graphs, bounded genus graphs, or, more generally, graphs with a fixed excluded minor. However, in order to apply the bidimensionality framework the considered problem needs to fulfill a special density property. Some well-known problems do not have this property, unfortunately, with probably the most prominent and important example being the Steiner Tree problem. Hence the question whether a subexponential-time parameterized algorithm for Steiner Tree on planar graphs exists has remained open. In this paper, we answer this question positively and develop an algorithm running in O(2^{O((k log k)^{2/3})}n) time and polynomial space, where k is the size of the Steiner tree and n is the number of vertices of the graph.
Our algorithm does not rely on tools from bidimensionality theory or graph minors theory, apart from Baker's classical approach. Instead, we introduce new tools and concepts to the study of the parameterized complexity of problems on sparse graphs.
Cite as
Marcin Pilipczuk, Michal Pilipczuk, Piotr Sankowski, and Erik Jan van Leeuwen. Subexponential-Time Parameterized Algorithm for Steiner Tree on Planar Graphs. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 353-364, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{pilipczuk_et_al:LIPIcs.STACS.2013.353,
author = {Pilipczuk, Marcin and Pilipczuk, Michal and Sankowski, Piotr and van Leeuwen, Erik Jan},
title = {{Subexponential-Time Parameterized Algorithm for Steiner Tree on Planar Graphs}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {353--364},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.353},
URN = {urn:nbn:de:0030-drops-39471},
doi = {10.4230/LIPIcs.STACS.2013.353},
annote = {Keywords: planar graph, Steiner tree, subexponential-time algorithms}
}
Document
The arithmetic complexity of tensor contractions
Abstract
We investigate the algebraic complexity of tensor calulus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable by arithmetic circuits. This gives a natural and robust characterization of this complexity class that despite its naturalness is not very well understood so far.
Cite as
Florent Capelli, Arnaud Durand, and Stefan Mengel. The arithmetic complexity of tensor contractions. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 365-376, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{capelli_et_al:LIPIcs.STACS.2013.365,
author = {Capelli, Florent and Durand, Arnaud and Mengel, Stefan},
title = {{The arithmetic complexity of tensor contractions}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {365--376},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.365},
URN = {urn:nbn:de:0030-drops-39481},
doi = {10.4230/LIPIcs.STACS.2013.365},
annote = {Keywords: algebraic complexity, arithmetic circuits, tensor calculus}
}
Document
Search versus Decision for Election Manipulation Problems
Abstract
Most theoretical definitions about the complexity of manipulating elections focus on the decision problem of recognizing which instances can be successfully manipulated, rather than the search problem of finding the successful manipulative actions. Since the latter is a far more natural goal for manipulators, that definitional focus may be misguided if these two complexities can differ. Our main result is that they probably do differ: If integer factoring is hard, then for election manipulation, election bribery, and some types of election control, there are election systems for which recognizing which instances can be successfully manipulated is in polynomial time but producing the successful manipulations cannot be done in polynomial time.
Cite as
Edith Hemaspaandra, Lane A. Hemaspaandra, and Curtis Menton. Search versus Decision for Election Manipulation Problems. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 377-388, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{hemaspaandra_et_al:LIPIcs.STACS.2013.377,
author = {Hemaspaandra, Edith and Hemaspaandra, Lane A. and Menton, Curtis},
title = {{Search versus Decision for Election Manipulation Problems}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {377--388},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.377},
URN = {urn:nbn:de:0030-drops-39498},
doi = {10.4230/LIPIcs.STACS.2013.377},
annote = {Keywords: Search vs. decision, application of structural complexity theory}
}
Document
Improved Bounds for Online Preemptive Matching
Abstract
When designing a preemptive online algorithm for the maximum matching problem, we wish to maintain a valid matching M while edges of the underlying graph are presented one after the other. When presented with an edge e, the algorithm should decide whether to augment the matching M by adding e (in which case e may be removed later on) or to keep M in its current form without adding e (in which case e is lost for good). The objective is to eventually hold a matching M with maximum weight.
The main contribution of this paper is to establish new lower and upper bounds on the competitive ratio achievable by preemptive online algorithms:
- We provide a lower bound of 1 + ln 2 \approx 1.693 on the competitive ratio of any randomized algorithm for the maximum cardinality matching problem, thus improving on the currently best known bound of e / (e-1) \approx 1.581 due to Karp, Vazirani, and Vazirani [STOC'90].
- We devise a randomized algorithm that achieves an expected competitive ratio of 5.356 for maximum weight matching. This finding demonstrates the power of randomization in this context, showing how to beat the tight bound of 3 + 2\sqrt{2} \approx 5.828 for deterministic algorithms, obtained by combining the 5.828 upper bound of McGregor [APPROX'05] and the recent 5.828 lower bound of Varadaraja [ICALP'11].
Cite as
Leah Epstein, Asaf Levin, Danny Segev, and Oren Weimann. Improved Bounds for Online Preemptive Matching. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 389-399, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{epstein_et_al:LIPIcs.STACS.2013.389,
author = {Epstein, Leah and Levin, Asaf and Segev, Danny and Weimann, Oren},
title = {{Improved Bounds for Online Preemptive Matching}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {389--399},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.389},
URN = {urn:nbn:de:0030-drops-39501},
doi = {10.4230/LIPIcs.STACS.2013.389},
annote = {Keywords: Online algorithms, matching, lower bound}
}
Document
Parameterized Matching in the Streaming Model
Abstract
We study the problem of parameterized matching in a stream where we want to output matches between a pattern of length m and the last m symbols of the stream before the next symbol arrives. Parameterized matching is a natural generalisation of exact matching where an arbitrary one-to-one relabelling of pattern symbols is allowed. We show how this problem can be solved in constant time per arriving stream symbol and sublinear, near optimal space with high probability. Our results are surprising and important: it has been shown that almost no streaming pattern matching problems can be solved (not even randomised) in less than Theta(m) space, with exact matching as the only known problem to have a sublinear, near optimal space solution. Here we demonstrate that a similar sublinear, near optimal space solution is achievable for an even more challenging problem.
Cite as
Markus Jalsenius, Benny Porat, and Benjamin Sach. Parameterized Matching in the Streaming Model. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 400-411, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{jalsenius_et_al:LIPIcs.STACS.2013.400,
author = {Jalsenius, Markus and Porat, Benny and Sach, Benjamin},
title = {{Parameterized Matching in the Streaming Model}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {400--411},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.400},
URN = {urn:nbn:de:0030-drops-39513},
doi = {10.4230/LIPIcs.STACS.2013.400},
annote = {Keywords: Pattern matching, streaming algorithms, randomized algorithms}
}
Document
Popular Matchings: Structure and Cheating Strategies
Abstract
We consider the cheating strategies for the popular matchings problem.
Let G = (\A \cup \p, E) be a bipartite graph where \A denotes a set of agents, p denotes a set of posts and the edges in E are ranked. Each agent ranks a subset of posts in an order of preference, possibly involving ties.
A matching M is popular if there exists no matching M' such that the number of agents that prefer M' to M exceeds the number of agents that prefer M to M'.
Consider a centralized market where agents submit their preferences and a central authority matches
agents to posts according to the notion of popularity.
Since a popular matching need not be unique, we assume that the central authority chooses an arbitrary popular matching. Let a_1 be the sole manipulative agent who is aware of the true
preference lists of all other agents.
The goal of a_1 is to falsify her preference list to get better always, that is, to improve the set of posts she gets matched to in the falsified instance.
We show that the optimal cheating strategy for a single agent to get better always can be computed
in O(m+n) time when preference lists are all strict and in O(\sqrt{n}m) time when preference lists are allowed to contain ties.
Here n = |\A| + |\p| and m = |E|.
To compute the cheating strategies, we develop a switching graph characterization of the popular matchings problem involving ties. The switching graph characterization was studied for the case of strict lists by McDermid and Irving (J. Comb. Optim. 2011) and was open for the case of ties. We show an O(\sqrt{n}m) time algorithm to compute the set of popular pairs using the switching graph.
These results are of independent interest and answer a part of the open questions posed by McDermid and Irving.
Cite as
Meghana Nasre. Popular Matchings: Structure and Cheating Strategies. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 412-423, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{nasre:LIPIcs.STACS.2013.412,
author = {Nasre, Meghana},
title = {{Popular Matchings: Structure and Cheating Strategies}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {412--423},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.412},
URN = {urn:nbn:de:0030-drops-39520},
doi = {10.4230/LIPIcs.STACS.2013.412},
annote = {Keywords: bipartite matchings, preferences, cheating strategies}
}
Document
Fooling One-Sided Quantum Protocols
Abstract
We use the venerable "fooling set" method to prove new lower bounds on the quantum communication complexity of various functions. Let f : X x Y -> {0,1} be a Boolean function, fool^1(f) its maximal fooling set size among 1-inputs, Q_1^*(f) its one-sided-error quantum communication complexity with prior entanglement, and NQ(f) its nondeterministic quantum communication complexity (without prior entanglement; this model is trivial with shared randomness or entanglement). Our main results are the following, where logs are to base 2:
- If the maximal fooling set is "upper triangular" (which is for instance the case for the equality, disjointness, and greater-than functions), then we have Q_1^*(f) >= 1/2 log fool^1(f) - 1/2, which (by superdense coding) is essentially optimal for functions like equality, disjointness, and greater-than. No super-constant lower bound for equality seems to follow from earlier techniques.
- For all f we have Q_1^*(f) >= 1/4 log fool^1(f) - 1/2.
- NQ(f) >= 1/2 log fool^1(f) + 1. We do not know if the factor 1/2 is needed in this result, but it cannot be replaced by 1: we give an example where NQ(f) \approx 0.613 log fool^1(f).
Cite as
Hartmut Klauck and Ronald de Wolf. Fooling One-Sided Quantum Protocols. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 424-433, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{klauck_et_al:LIPIcs.STACS.2013.424,
author = {Klauck, Hartmut and de Wolf, Ronald},
title = {{Fooling One-Sided Quantum Protocols}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {424--433},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.424},
URN = {urn:nbn:de:0030-drops-39539},
doi = {10.4230/LIPIcs.STACS.2013.424},
annote = {Keywords: Quantum computing, communication complexity, fooling set, lower bound}
}
Document
Explicit relation between all lower bound techniques for quantum query complexity
Abstract
The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the polynomial method to the multiplicative adversary method. The proof goes by extending the polynomial method from Boolean functions to quantum state generation problems. In the process, the bound is even strengthened. We then show that this extended polynomial method is a special case of the multiplicative adversary method with an adversary matrix that is independent of the function. This new result therefore provides insight on the reason why in some cases the adversary method is stronger than the polynomial method. It also reveals a clear picture of the relation between the different lower bound techniques, as it implies that all known techniques reduce to the multiplicative adversary method.
Cite as
Loïck Magnin and Jérémie Roland. Explicit relation between all lower bound techniques for quantum query complexity. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 434-445, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{magnin_et_al:LIPIcs.STACS.2013.434,
author = {Magnin, Lo\"{i}ck and Roland, J\'{e}r\'{e}mie},
title = {{Explicit relation between all lower bound techniques for quantum query complexity}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {434--445},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.434},
URN = {urn:nbn:de:0030-drops-39548},
doi = {10.4230/LIPIcs.STACS.2013.434},
annote = {Keywords: Quantum computation, lower bound, adversary method, polynomial method}
}
Document
Optimal quantum query bounds for almost all Boolean functions
Abstract
We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis (A. Ambainis, 1999), and shows that van Dam's oracle interrogation (W. van Dam, 1998) is essentially optimal for almost all functions. Our proof uses the fact that the acceptance probability of a T-query algorithm can be written as the sum of squares of degree-T polynomials.
Cite as
Andris Ambainis, Arturs Backurs, Juris Smotrovs, and Ronald de Wolf. Optimal quantum query bounds for almost all Boolean functions. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 446-453, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{ambainis_et_al:LIPIcs.STACS.2013.446,
author = {Ambainis, Andris and Backurs, Arturs and Smotrovs, Juris and de Wolf, Ronald},
title = {{Optimal quantum query bounds for almost all Boolean functions}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {446--453},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.446},
URN = {urn:nbn:de:0030-drops-39557},
doi = {10.4230/LIPIcs.STACS.2013.446},
annote = {Keywords: Quantum computing, query complexity, lower bounds, polynomial method}
}
Document
Streaming Complexity of Checking Priority Queues
Abstract
This work is in the line of designing efficient checkers for testing the reliability of some massive data structures. Given a sequential access to the insert/extract operations on such a structure, one would like to decide, a posteriori only, if it corresponds to the evolution of a reliable structure.
In a context of massive data, one would like to minimize both the amount of reliable memory of the checker and the number of passes on the sequence of operations.
Chu, Kannan and McGregor (M. Chu, S. Kannan, and A. McGregor, 2007) initiated the study of checking priority queues in this setting. They showed that the use of timestamps allows to check a priority queue with a single pass and memory space \tilde{\Order}(\sqrt{N}). Later, Chakrabarti, Cormode, Kondapally and McGregor (A. Chakrabarti, G. Cormode, R. Kondapally, and A. McGregor, 2010) removed the use of timestamps, and proved that more passes do not help.
We show that, even in the presence of timestamps, more passes do not help, solving an open problem
of (M. Chu, S. Kannan, and A. McGregor, 2007; A. Chakrabarti, G. Cormode, R. Kondapally, and A. McGregor). On the other hand, we show that a second pass, but in reverse direction shrinks the memory space to \tilde{\Order}((\log N)^2), extending a phenomenon the first time observed by Magniez, Mathieu and Nayak (F. Magniez, C. Mathieu, and A. Nayak, 2010) for checking well-parenthesized expressions.
Cite as
Nathanael Francois and Frédéric Magniez. Streaming Complexity of Checking Priority Queues. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 454-465, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{francois_et_al:LIPIcs.STACS.2013.454,
author = {Francois, Nathanael and Magniez, Fr\'{e}d\'{e}ric},
title = {{Streaming Complexity of Checking Priority Queues}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {454--465},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.454},
URN = {urn:nbn:de:0030-drops-39561},
doi = {10.4230/LIPIcs.STACS.2013.454},
annote = {Keywords: Streaming Algorithms, Communication Complexity, Priority Queue}
}
Document
Deterministic algorithms for skewed matrix products
Abstract
Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new deterministic matrix multiplication algorithms.
Motivated by applications in data mining, we first consider the case of real-valued, nonnegative n-by-n input matrices A and B, and show how to obtain a deterministic approximation of the weights of individual entries, as well as the entrywise p-norm, of the product AB. The algorithm is simple, space efficient and runs in one pass over the input matrices. For a user defined b \in (0, n^2) the algorithm runs in time O(nb + n Sort(n)) and space O(n + b) and returns an approximation of the entries of AB within an additive factor of ||AB||_{E1}/b, where ||C||_{E1} = sum_{i, j} |C_{ij}| is the entrywise 1-norm of a matrix C and Sort(n) is the time required to sort n real numbers in linear space. Building upon a result by Berinde et al. we show that for skewed matrix products (a common situation in many real-life applications) the algorithm is more efficient and achieves better approximation guarantees than previously known randomized algorithms.
When the input matrices are not restricted to nonnegative entries, we present a new deterministic group testing algorithm detecting nonzero entries in the matrix product with large absolute value. The algorithm is clearly outperformed by randomized matrix multiplication algorithms, but as a byproduct we obtain the first O(n^{2 + epsilon})-time deterministic algorithm for matrix products with O(sqrt(n)) nonzero entries.
Cite as
Konstantin Kutzkov. Deterministic algorithms for skewed matrix products. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 466-477, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{kutzkov:LIPIcs.STACS.2013.466,
author = {Kutzkov, Konstantin},
title = {{Deterministic algorithms for skewed matrix products}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {466--477},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.466},
URN = {urn:nbn:de:0030-drops-39577},
doi = {10.4230/LIPIcs.STACS.2013.466},
annote = {Keywords: approximate deterministic memory-efficient matrix multiplication}
}
Document
The Simulated Greedy Algorithm for Several Submodular Matroid Secretary Problems
Abstract
We study the matroid secretary problems with submodular valuation functions. In these problems, the elements arrive in random order. When one element arrives, we have to make an immediate and irrevocable decision on whether to accept it or not. The set of accepted elements must form an independent set in a predefined matroid. Our objective is to maximize the value of the accepted elements. In this paper, we focus on the case that the valuation function is a non-negative and monotonically non-decreasing submodular function.
We introduce a general algorithm for such submodular matroid secretary problems. In particular, we obtain constant competitive algorithms for the cases of laminar matroids and transversal
matroids. Our algorithms can be further applied to any independent set system defined by the intersection of a constant number of laminar matroids, while still achieving constant competitive ratios. Notice that laminar matroids generalize uniform matroids and partition matroids.
On the other hand, when the underlying valuation function is linear, our algorithm achieves a competitive ratio of 9.6 for laminar matroids, which significantly improves the previous
result.
Cite as
Tengyu Ma, Bo Tang, and Yajun Wang. The Simulated Greedy Algorithm for Several Submodular Matroid Secretary Problems. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 478-489, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{ma_et_al:LIPIcs.STACS.2013.478,
author = {Ma, Tengyu and Tang, Bo and Wang, Yajun},
title = {{The Simulated Greedy Algorithm for Several Submodular Matroid Secretary Problems}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {478--489},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.478},
URN = {urn:nbn:de:0030-drops-39586},
doi = {10.4230/LIPIcs.STACS.2013.478},
annote = {Keywords: secretary problem, submodular function, matroid, online algorithm}
}
Document
Hardness of Conjugacy, Embedding and Factorization of multidimensional Subshifts of Finite Type
Abstract
Subshifts of finite type are sets of colorings of the plane defined by local constraints. They can be seen as a discretization of continuous dynamical systems. We investigate here the hardness of deciding factorization, conjugacy and embedding of subshifts of finite type (SFTs) in dimension d > 1. In particular, we prove that the factorization problem is Sigma^0_3-complete and that the conjugacy and embedding problems are Sigma^0_1-complete in the arithmetical hierarchy.
Cite as
Emmanuel Jeandel and Pascal Vanier. Hardness of Conjugacy, Embedding and Factorization of multidimensional Subshifts of Finite Type. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 490-501, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{jeandel_et_al:LIPIcs.STACS.2013.490,
author = {Jeandel, Emmanuel and Vanier, Pascal},
title = {{Hardness of Conjugacy, Embedding and Factorization of multidimensional Subshifts of Finite Type}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {490--501},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.490},
URN = {urn:nbn:de:0030-drops-39592},
doi = {10.4230/LIPIcs.STACS.2013.490},
annote = {Keywords: Subshifts, Computability, Factorization, Embedding, Conjugacy}
}
Document
The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable
Abstract
We prove that a semigroup generated by a reversible two-state Mealy automaton is either finite or free of rank 2. This fact leads to the decidability of finiteness for groups generated by two-state or two-letter invertible-reversible Mealy automata and to the decidability of freeness for semigroups generated by two-state invertible-reversible Mealy automata.
Cite as
Ines Klimann. The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 502-513, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{klimann:LIPIcs.STACS.2013.502,
author = {Klimann, Ines},
title = {{The finiteness of a group generated by a 2-letter invertible-reversible Mealy automaton is decidable}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {502--513},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.502},
URN = {urn:nbn:de:0030-drops-39605},
doi = {10.4230/LIPIcs.STACS.2013.502},
annote = {Keywords: Mealy automata, automaton semigroups, decidability of finiteness, decidability of freeness, Nerode equivalence}
}
Document
Extended Abstract
Mortality of Iterated Piecewise Affine Functions over the Integers: Decidability and Complexity (Extended Abstract)
Abstract
In the theory of discrete-time dynamical systems, one studies the limiting behaviour of processes defined by iterating a fixed function f over a given space. A much-studied case involves piecewise affine functions on R^n. Blondel et al. (2001) studied the decidability of questions such as mortality for such functions with rational coefficients. Mortality means that every trajectory includes a 0; if the iteration is seen as a loop while (x \ne 0) x := f(x), mortality means that the loop is guaranteed to terminate.
Blondel et al. proved that the problems are undecidable when the dimension n of the state space is at least two. They assume that the variables range over the rationals; this is an essential assumption. From a program analysis (and discrete Computability) viewpoint, it would be more interesting to consider integer-valued variables.
This paper establishes (un)decidability results for the integer setting. We show that also over integers, undecidability (moreover, Pi^0_2 completeness) begins at two dimensions. We further investigate the effect of several restrictions on the iterated functions. Specifically, we consider bounding the size of the partition defining f, and restricting the coefficients of the linear components. In the decidable cases, we give complexity results. The complexity is PTIME for affine functions, but for piecewise-affine ones it is PSPACE-complete. The undecidability proofs use some variants of the Collatz problem, which may be of independent interest.
Cite as
Amir M. Ben-Amram. Mortality of Iterated Piecewise Affine Functions over the Integers: Decidability and Complexity (Extended Abstract). In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 514-525, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{benamram:LIPIcs.STACS.2013.514,
author = {Ben-Amram, Amir M.},
title = {{Mortality of Iterated Piecewise Affine Functions over the Integers: Decidability and Complexity}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {514--525},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.514},
URN = {urn:nbn:de:0030-drops-39615},
doi = {10.4230/LIPIcs.STACS.2013.514},
annote = {Keywords: discrete-time dynamical systems, termination, Collatz problem}
}
Document
On the practically interesting instances of MAXCUT
Abstract
For many optimization problems, the instances of practical interest often occupy just a tiny part of the algorithm's space of instances.
Following (Y. Bilu and N. Linial, 2010), we apply this perspective to MAXCUT, viewed as a clustering problem. Using a variety of techniques, we investigate practically interesting instances of this problem. Specifically, we show how to solve in polynomial time distinguished, metric, expanding and dense instances of MAXCUT under mild stability assumptions. In particular, (1 + epsilon)-stability (which is optimal) suffices for metric and dense MAXCUT. We also show how to solve in polynomial time Omega(sqrt(n))-stable instances of MAXCUT, substantially improving the best previously known result.
Cite as
Yonatan Bilu, Amit Daniely, Nati Linial, and Michael Saks. On the practically interesting instances of MAXCUT. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 526-537, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{bilu_et_al:LIPIcs.STACS.2013.526,
author = {Bilu, Yonatan and Daniely, Amit and Linial, Nati and Saks, Michael},
title = {{On the practically interesting instances of MAXCUT}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {526--537},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.526},
URN = {urn:nbn:de:0030-drops-39625},
doi = {10.4230/LIPIcs.STACS.2013.526},
annote = {Keywords: MAXCUT, Clustering, Hardness in practice, Stability, Non worst-case analysis}
}
Document
First Fit bin packing: A tight analysis
Abstract
In the bin packing problem we are given an instance consisting of a sequence of items with sizes between 0 and 1. The objective is to pack these items into the smallest possible number of bins of unit size. FirstFit algorithm packs each item into the first bin where it fits, possibly opening a new bin if the item cannot fit into any currently open bin. In early seventies it was shown that the asymptotic approximation ratio of FirstFit bin packing is equal to 1.7.
We prove that also the absolute approximation ratio for FirstFit bin packing is exactly 1.7. This means that if the optimum needs OPT bins, FirstFit always uses at most \lfloor 1.7 OPT \rfloor bins.
Furthermore we show matching lower bounds for a majority of values of OPT, i.e., we give instances on which FirstFit uses exactly \lfloor 1.7 OPT \rfloor bins.
Such matching upper and lower bounds were previously known only for finitely many small values of OPT. The previous published bound on the absolute approximation ratio of FirstFit was 12/7 \approx 1.7143. Recently a bound of 101/59 \approx 1.7119 was claimed.
Cite as
György Dósa and Jiri Sgall. First Fit bin packing: A tight analysis. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 538-549, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{dosa_et_al:LIPIcs.STACS.2013.538,
author = {D\'{o}sa, Gy\"{o}rgy and Sgall, Jiri},
title = {{First Fit bin packing: A tight analysis}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {538--549},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.538},
URN = {urn:nbn:de:0030-drops-39630},
doi = {10.4230/LIPIcs.STACS.2013.538},
annote = {Keywords: Approximation algorithms, online algorithms, bin packing, First Fit}
}
Document
Constrained Binary Identification Problem
Abstract
We consider the problem of building a binary decision tree, to locate an object within a set by way of the least number of membership queries. This problem is equivalent to the "20 questions game" of information theory and is closely related to lossless source compression. If any query is admissible, Huffman coding is optimal with close to H[P] questions on average, the entropy of the prior distribution P over objects. However, in many realistic scenarios, there are constraints on which queries can be asked, and solving the problem optimally is NP-hard.
We provide novel polynomial time approximation algorithms where constraints are defined in terms of "graph", general "cost", and "submodular" functions. In particular, we show that under graph constraints, there exists a constant approximation algorithm for locating the target in the set. We then extend our approach for scenarios where the constraints are defined in terms of general cost functions that depend only on the size of the query and provide an approximation algorithm that can find the target within O(log(log n)) gap from the cost of the optimum algorithm. Submodular functions come as a natural generalization of cost functions with decreasing marginals. Under submodular set constraints, we devise an approximation algorithm that can find the target within O(log n) gap from the cost of the optimum algorithm. The proposed algorithms are greedy in a sense that at each step they select a query that most evenly splits the set without violating the underlying constraints. These results can be applied to network tomography, active learning and interactive content search.
Cite as
Amin Karbasi and Morteza Zadimoghaddam. Constrained Binary Identification Problem. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 550-561, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{karbasi_et_al:LIPIcs.STACS.2013.550,
author = {Karbasi, Amin and Zadimoghaddam, Morteza},
title = {{Constrained Binary Identification Problem}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {550--561},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.550},
URN = {urn:nbn:de:0030-drops-39647},
doi = {10.4230/LIPIcs.STACS.2013.550},
annote = {Keywords: Network Tomography, Binary Identification Problem, Approximation Algorithms, Graph Algorithms, Tree Search Strategies, Entropy}
}
Document
Regular languages of thin trees
Abstract
An infinite tree is called thin if it contains only countably many infinite branches. Thin trees can be seen as intermediate structures between infinite words and infinite trees. In this work we investigate properties of regular languages of thin trees.
Our main tool is an algebra suitable for thin trees. Using this framework we characterize various classes of regular languages: commutative, open in the standard topology, closed under two variants of bisimulational equivalence, and definable in WMSO logic among all trees.
We also show that in various meanings thin trees are not as rich as all infinite trees. In particular we observe a parity index collapse to level (1,3) and a topological complexity collapse to co-analytic sets. Moreover, a gap property is shown: a regular language of thin trees is either WMSO-definable among all trees or co-analytic-complete.
Cite as
Mikolaj Bojanczyk, Tomasz Idziaszek, and Michal Skrzypczak. Regular languages of thin trees. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 562-573, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{bojanczyk_et_al:LIPIcs.STACS.2013.562,
author = {Bojanczyk, Mikolaj and Idziaszek, Tomasz and Skrzypczak, Michal},
title = {{Regular languages of thin trees}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {562--573},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.562},
URN = {urn:nbn:de:0030-drops-39655},
doi = {10.4230/LIPIcs.STACS.2013.562},
annote = {Keywords: infinite trees, regular languages, effective characterizations, topological complexity}
}
Document
Approximate comparison of distance automata
Abstract
Distance automata are automata weighted over the semiring (\mathbb{N} \cup \infty,\min,+) (the tropical semiring). Such automata compute functions from words to \mathbb{N} \cup \infty such as the number of occurrences of a given letter. It is known that testing f <= g is an undecidable problem for f,g computed by distance automata. The main contribution of this paper is to show that an approximation of this problem becomes decidable.
We present an algorithm which, given epsilon > 0 and two functions f,g computed by distance automata, answers "yes" if f <= (1-epsilon) g, "no" if $f \not\leq g$, and may answer "yes" or "no" in all other cases. This result highly refines previously known decidability results of the same type.
The core argument behind this quasi-decision procedure is an algorithm which is able to provide an approximated finite presentation to the closure under products of sets of matrices over the tropical semiring.
We also provide another theorem, of affine domination, which shows that previously known decision procedures for cost-automata have an improved precision when used over distance automata.
Cite as
Thomas Colcombet and Laure Daviaud. Approximate comparison of distance automata. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 574-585, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{colcombet_et_al:LIPIcs.STACS.2013.574,
author = {Colcombet, Thomas and Daviaud, Laure},
title = {{Approximate comparison of distance automata}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {574--585},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.574},
URN = {urn:nbn:de:0030-drops-39667},
doi = {10.4230/LIPIcs.STACS.2013.574},
annote = {Keywords: Distance automata, tropical semiring, decidability, cost functions}
}
Document
The Rank of Tree-Automatic Linear Orderings
Abstract
A tree-automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. The finite condensation rank (FC-rank) of a linear ordering measures how far it is away from being dense. We prove that the FC-rank of every tree-automatic linear ordering is below omega^omega. This generalises Delhommé's result that each tree-automatic ordinal is less than omega^omega^omega. Furthermore, we show an analogue for tree-automatic linear orderings where the branching complexity of the trees involved is bounded.
Cite as
Martin Huschenbett. The Rank of Tree-Automatic Linear Orderings. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 586-597, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{huschenbett:LIPIcs.STACS.2013.586,
author = {Huschenbett, Martin},
title = {{The Rank of Tree-Automatic Linear Orderings}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {586--597},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.586},
URN = {urn:nbn:de:0030-drops-39672},
doi = {10.4230/LIPIcs.STACS.2013.586},
annote = {Keywords: tree-automatic structures, linear orderings, finite condensation rank, computable model theory}
}
Document
A general framework for the realistic analysis of sorting and searching algorithms. Application to some popular algorithms
Abstract
We describe a general framework for realistic analysis of sorting and searching algorithms, and we apply it to the average-case analysis of five basic algorithms: three sorting algorithms (QuickSort, InsertionSort, BubbleSort) and two selection algorithms (QuickMin and SelectionMin). Usually, the analysis deals with the mean number of key comparisons, but, here, we view keys as words produced by the same source, which are compared via their symbols in the lexicographic order. The "realistic" cost of the algorithm is now the total number of symbol comparisons performed by the algorithm, and, in this context, the average-case analysis aims to providee stimates for the mean number of symbol comparisons used by the algorithm. For sorting algorithms, and with respect to key comparisons, the average-case complexity of QuickSort is asymptotic to 2n log n, InsertionSort to n^2/4 and BubbleSort to n^2/2. With respect to symbol comparisons, we prove that their average-case complexity becomes Theta(n log^2n), Theta(n^2), Theta (n^2 log n). For selection algorithms, and with respect to key comparisons, the average-case complexity of QuickMin is asymptotic to 2n, of SelectionMin is n - 1. With respect to symbol comparisons, we prove that their average-case complexity remains Theta(n). In these five cases, we describe the dominant constants which exhibit the probabilistic behaviour of the source (namely, entropy, and various notions of coincidence) with respect to the algorithm.
Cite as
Julien Clément, Thu Hien Nguyen Thi, and Brigitte Vallée. A general framework for the realistic analysis of sorting and searching algorithms. Application to some popular algorithms. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 598-609, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{clement_et_al:LIPIcs.STACS.2013.598,
author = {Cl\'{e}ment, Julien and Nguyen Thi, Thu Hien and Vall\'{e}e, Brigitte},
title = {{A general framework for the realistic analysis of sorting and searching algorithms. Application to some popular algorithms}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {598--609},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.598},
URN = {urn:nbn:de:0030-drops-39681},
doi = {10.4230/LIPIcs.STACS.2013.598},
annote = {Keywords: Probabilistic analysis of algorithms, Sorting and searching algorithms, Pattern matching, Permutations, Information theory, Rice formula, Asymptotic e}
}
Document
Search using queries on indistinguishable items
Abstract
We investigate the problem of determining a set S of k indistinguishable integers in the range [1, n].
The algorithm is allowed to query an integer q \in [1,n], and receive a response comparing this integer to an integer randomly chosen from S. The algorithm has no control over which element of S the query q is compared to. We show tight bounds for this problem. In particular, we show that in the natural regime where k <= n, the optimal number of queries to attain n^{-Omega(1)} error probability is Theta(k^3 log n). In the regime where k > n, the optimal number of queries is Theta(n^2 k log n).
Our main technical tools include the use of information theory to derive the lower bounds, and the application of noisy binary search in the spirit of Feige, Raghavan, Peleg, and Upfal (1994). In particular, our lower bound technique is likely to be applicable in other situations that involve search under uncertainty.
Cite as
Mark Braverman and Gal Oshri. Search using queries on indistinguishable items. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 610-621, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{braverman_et_al:LIPIcs.STACS.2013.610,
author = {Braverman, Mark and Oshri, Gal},
title = {{Search using queries on indistinguishable items}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {610--621},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.610},
URN = {urn:nbn:de:0030-drops-39696},
doi = {10.4230/LIPIcs.STACS.2013.610},
annote = {Keywords: Search, Noisy Search, Information Theory, Query Complexity}
}
Document
Pebbling, Entropy and Branching Program Size Lower Bounds
Abstract
We contribute to the program of proving lower bounds on the size of branching programs solving the Tree Evaluation Problem introduced in (Stephen A. Cook, Pierre McKenzie, Dustin Wehr, Mark Braverman, and Rahul Santhanam, 2012). Proving an exponential lower bound for the size of the non-deterministic thrifty branching programs would separate NL from P under the thrifty hypothesis. In this context, we consider a restriction of non-deterministic thrifty branching programs called bitwise-independence. We show that any bitwise-independent non-deterministic thrifty branching program solving BT_2(h,k) must have at least 1/2 k^{h/2} states. Prior to this work, lower bounds were known for general branching programs only for fixed heights h=2,3,4 (Stephen A. Cook, Pierre McKenzie, Dustin Wehr, Mark Braverman, and Rahul Santhanam, 2012). Our lower bounds are also tight (up to a factor of k), since the known (Stephen A. Cook, Pierre McKenzie, Dustin Wehr, Mark Braverman, and Rahul Santhanam, 2012) non-deterministic thrifty branching programs for this problem of size O(k^{h/2+1}) are bitwise-independent. We prove our results by associating a fractional pebbling strategy with any bitwise-independent non-deterministic thrifty branching program solving the Tree Evaluation Problem. Such a connection was not known previously even for fixed heights.
Our main technique is the entropy method introduced by Jukna and Zak (S. Jukna and S. Žák, 2003) originally in the context of proving lower bounds for read-once branching programs. We also show that the previous lower bounds known (Stephen A. Cook, Pierre McKenzie, Dustin Wehr, Mark Braverman, and Rahul Santhanam, 2012) for deterministic branching programs for Tree Evaluation Problem can be obtained using this approach. Using this method, we also show tight lower bounds for any k-way deterministic branching program solving Tree Evaluation Problem when the instances are restricted to have the same group operation in all internal nodes.
Cite as
Balagopal Komarath and Jayalal M. N. Sarma. Pebbling, Entropy and Branching Program Size Lower Bounds. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 622-633, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{komarath_et_al:LIPIcs.STACS.2013.622,
author = {Komarath, Balagopal and Sarma, Jayalal M. N.},
title = {{Pebbling, Entropy and Branching Program Size Lower Bounds}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {622--633},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.622},
URN = {urn:nbn:de:0030-drops-39709},
doi = {10.4230/LIPIcs.STACS.2013.622},
annote = {Keywords: Pebbling, Entropy Method, Branching Programs, Size Lower Bounds.}
}
Document
Advice Lower Bounds for the Dense Model Theorem
Abstract
We prove a lower bound on the amount of nonuniform advice needed by black-box reductions for the Dense Model Theorem of Green, Tao, and Ziegler, and of Reingold, Trevisan, Tulsiani, and Vadhan. The latter theorem roughly says that for every distribution D that is delta-dense in a distribution that is epsilon'-indistinguishable from uniform, there exists a "dense model" for D, that is, a distribution that is delta-dense in the uniform distribution and is epsilon-indistinguishable from D. This epsilon-indistinguishability is with respect to an arbitrary small class of functions F. For the natural case where epsilon' >= Omega(epsilon delta) and epsilon >= delta^{O(1)}, our lower bound implies that Omega(sqrt{(1/epsilon)log(1/delta)} log|F|) advice bits are necessary. There is only a polynomial gap between our lower bound and the best upper bound for this case (due to Zhang), which is O((1/epsilon^2)log(1/delta) log|F|). Our lower bound can be viewed as an analog of list size lower bounds for list-decoding of error-correcting codes, but for "dense model decoding" instead. Our proof introduces some new techniques which may be of independent interest, including an analysis of a majority of majorities of p-biased bits. The latter analysis uses an extremely tight lower bound on the tail of the binomial distribution, which we could not find in the literature.
Cite as
Thomas Watson. Advice Lower Bounds for the Dense Model Theorem. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 634-645, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{watson:LIPIcs.STACS.2013.634,
author = {Watson, Thomas},
title = {{Advice Lower Bounds for the Dense Model Theorem}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {634--645},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.634},
URN = {urn:nbn:de:0030-drops-39717},
doi = {10.4230/LIPIcs.STACS.2013.634},
annote = {Keywords: Pseudorandomness, advice lower bounds, dense model theorem}
}
Document
Author Index
Abstract
Author Index.
Cite as
Natacha Portier and Thomas Wilke. Author Index. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 646-647, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@InProceedings{portier_et_al:LIPIcs.STACS.2013.646,
author = {Portier, Natacha and Wilke, Thomas},
title = {{Author Index}},
booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
pages = {646--647},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-50-7},
ISSN = {1868-8969},
year = {2013},
volume = {20},
editor = {Portier, Natacha and Wilke, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.646},
URN = {urn:nbn:de:0030-drops-39729},
doi = {10.4230/LIPIcs.STACS.2013.646},
annote = {Keywords: Author Index}
}