Volume
LIPIcs, Volume 3
26th International Symposium on Theoretical Aspects of Computer Science
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
Event
STACS 2009, February 26-28, 2009, Freiburg, GermanyEditors
Publication Details
- published at: 2009-02-19
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-939897-09-5
- DBLP: db/conf/stacs/stacs2009
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Document
Complete Volume
LIPIcs, Volume 3, STACS'09, Complete Volume
Abstract
LIPIcs, Volume 3, STACS'09, Complete Volume
Cite as
26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@Proceedings{albers_et_al:LIPIcs.STACS.2009,
title = {{LIPIcs, Volume 3, STACS'09, Complete Volume}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2013},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009},
URN = {urn:nbn:de:0030-drops-40975},
doi = {10.4230/LIPIcs.STACS.2009},
annote = {Keywords: LIPIcs, Volume 3, STACS'09, Complete Volume}
}
Document
Front Matter
Preface -- 26th International Symposium on Theoretical Aspects of Computer Science
Abstract
The interest in STACS has remained at a high level over the past years. The STACS 2009 call for papers led to over 280 submissions from 41 countries. Each paper was assigned to three program committee members. The program committee held a two-week electronic meeting at the beginning of November and selected 54 papers. As co-chairs of the program committee, we would like to sincerely thank its members and the many external referees for their valuable work. The overall very high quality of the submissions made the selection a difficult task.
We would like to express our thanks to the three invited speakers, Monika Henzinger, Jean-Eric Pin and Nicole Schweikardt, for their contributions to the proceedings.
Special thanks are due to A. Voronkov for his EasyChair software (www.easychair.org). Moreover we would like to thank Sonja Lauer for preparing the conference proceedings and continuous help throughout the conference organization.
For the second time this year's STACS proceedings are published in electronic form. A printed version was also available at the conference, with ISBN 978-3-939897-09-5. The electronic proceedings are available through several portals, and in particular through HAL and DROPS. HAL is an electronic repository managed by several French research agencies, and DROPS is the Dagstuhl Research Online Publication Server. We want to thank both these servers for hosting the proceedings of STACS and guaranteeing them perennial availability. The rights on the articles in the proceedings are kept with the authors and the papers are available freely, under a Creative Commons license (seewww.stacs-conf.org/faq.html for more details).
Cite as
26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. i-vii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{albers_et_al:LIPIcs.STACS.2009.1858,
author = {Albers, Susanne and Marion, Jean-Yves},
title = {{Preface -- 26th International Symposium on Theoretical Aspects of Computer Science}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {i--vii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1858},
URN = {urn:nbn:de:0030-drops-18584},
doi = {10.4230/LIPIcs.STACS.2009.1858},
annote = {Keywords: Symposium, Theoretical computer science, Algorithms and data structures, Automata and formal languages, Computational and structural complex}
}
Document
A Comparison of Techniques for Sampling Web Pages
Abstract
As the World Wide Web is growing rapidly, it is getting increasingly challenging to gather representative information about it. Instead of crawling the web exhaustively one has to resort to other techniques like sampling to determine the properties of the web. A uniform random sample of the web would be useful to determine the percentage of web pages in a specific language, on a topic or in a top level domain. Unfortunately, no approach has been shown to sample the web pages in an unbiased way. Three promising web sampling algorithms are based on random walks. They each have been evaluated individually, but making a comparison on different data sets is not possible. We directly compare these algorithms in this paper. We performed three random walks on the web under the same conditions and analyzed their outcomes in detail. We discuss the strengths and the weaknesses of each algorithm and propose improvements based on experimental results.
Cite as
Eda Baykan, Monika Henzinger, Stefan F. Keller, Sebastian de Castelberg, and Markus Kinzler. A Comparison of Techniques for Sampling Web Pages. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 13-30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{baykan_et_al:LIPIcs.STACS.2009.1809,
author = {Baykan, Eda and Henzinger, Monika and Keller, Stefan F. and de Castelberg, Sebastian and Kinzler, Markus},
title = {{A Comparison of Techniques for Sampling Web Pages}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {13--30},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1809},
URN = {urn:nbn:de:0030-drops-18091},
doi = {10.4230/LIPIcs.STACS.2009.1809},
annote = {Keywords: Random walks, Sampling web pages}
}
Document
Profinite Methods in Automata Theory
Abstract
This survey paper presents the success story of the topological approach to automata theory. It is based on profinite topologies, which are built from finite topogical spaces. The survey includes several concrete applications to automata theory.
Cite as
Jean-Eric Pin. Profinite Methods in Automata Theory. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 31-50, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{pin:LIPIcs.STACS.2009.1856,
author = {Pin, Jean-Eric},
title = {{Profinite Methods in Automata Theory}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {31--50},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1856},
URN = {urn:nbn:de:0030-drops-18561},
doi = {10.4230/LIPIcs.STACS.2009.1856},
annote = {Keywords: Profinite topology, Regular languages, Uniform space, Finite automata}
}
Document
Lower Bounds for Multi-Pass Processing of Multiple Data Streams
Abstract
This paper gives a brief overview of computation models for data stream processing, and it introduces a new model for multi-pass processing of multiple streams, the so-called \emph{mp2s-automata}. Two algorithms for solving the set disjointness problem with these automata are presented. The main technical contribution of this paper is the proof of a lower bound on the size of memory and the number of heads that are required for solving the set disjointness problem with mp2s-automata.
Cite as
Nicole Schweikardt. Lower Bounds for Multi-Pass Processing of Multiple Data Streams. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 51-62, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{schweikardt:LIPIcs.STACS.2009.1857,
author = {Schweikardt, Nicole},
title = {{Lower Bounds for Multi-Pass Processing of Multiple Data Streams}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {51--62},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1857},
URN = {urn:nbn:de:0030-drops-18575},
doi = {10.4230/LIPIcs.STACS.2009.1857},
annote = {Keywords: Data streams, Lower bounds, Machine models, Automata, The set disjointness problem}
}
Document
Shortest Paths Avoiding Forbidden Subpaths
Abstract
In this paper we study a variant of the shortest path problem in graphs: given a weighted graph $G$ and vertices $s$ and $t$, and given a set $X$ of forbidden paths in $G$, find a shortest $s$-$t$ path $P$ such that no path in $X$ is a subpath of $P$. Path $P$ is allowed to repeat vertices and edges. We call each path in $X$ an \emph{exception}, and our desired path a \emph{shortest exception avoiding path}. We formulate a new version of the problem where the algorithm has no a priori knowledge of $X$, and finds out about an exception $x \in X$ only when a path containing $x$ fails. This situation arises in computing shortest paths in optical networks. We give an algorithm that finds a shortest exception avoiding path in time polynomial in $|G|$ and $|X|$. The main idea is to run Dijkstra's algorithm incrementally after replicating vertices when an exception is discovered.
Cite as
Mustaq Ahmed and Anna Lubiw. Shortest Paths Avoiding Forbidden Subpaths. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 63-74, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{ahmed_et_al:LIPIcs.STACS.2009.1831,
author = {Ahmed, Mustaq and Lubiw, Anna},
title = {{Shortest Paths Avoiding Forbidden Subpaths}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {63--74},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1831},
URN = {urn:nbn:de:0030-drops-18318},
doi = {10.4230/LIPIcs.STACS.2009.1831},
annote = {Keywords: Algorithms and data structures, Graph algorithms, Optical networks}
}
Document
Generating Shorter Bases for Hard Random Lattices
Abstract
We revisit the problem of generating a ``hard'' random lattice together with a basis of relatively short vectors. This problem has gained in importance lately due to new cryptographic schemes that use such a procedure for generating public/secret key pairs. In these applications, a shorter basis directly corresponds to milder underlying complexity assumptions and smaller key sizes.
The contributions of this work are twofold. First, using the \emph{Hermite normal form} as an organizing principle, we simplify and generalize an approach due to Ajtai (ICALP 1999). Second, we improve the construction and its analysis in several ways, most notably by tightening the length of the output basis essentially to the optimum value.
Cite as
Joel Alwen and Chris Peikert. Generating Shorter Bases for Hard Random Lattices. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 75-86, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{alwen_et_al:LIPIcs.STACS.2009.1832,
author = {Alwen, Joel and Peikert, Chris},
title = {{Generating Shorter Bases for Hard Random Lattices}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {75--86},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1832},
URN = {urn:nbn:de:0030-drops-18327},
doi = {10.4230/LIPIcs.STACS.2009.1832},
annote = {Keywords: Lattices, Random, Short basis, Average-case hardness, Hermite normal form, Cryptography}
}
Document
Quantum Query Complexity of Multilinear Identity Testing
Abstract
Motivated by the quantum algorithm for testing commutativity of black-box groups (Magniez and Nayak, 2007), we study the following problem: Given a black-box finite ring by an additive generating set and a multilinear polynomial over that ring, also accessed as a black-box function (we allow the indeterminates of the polynomial to be commuting or noncommuting), we study the problem of testing if the polynomial is an \emph{identity} for the given ring. We give a quantum algorithm with query complexity sub-linear in the number of generators for the ring, when the number of indeterminates of the input polynomial is small (ideally a constant). Towards a lower bound, we also show a reduction from a version of the collision problem (which is well studied in quantum computation) to a variant of this problem.
Cite as
Vikraman Arvind and Partha Mukhopadhyay. Quantum Query Complexity of Multilinear Identity Testing. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 87-98, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{arvind_et_al:LIPIcs.STACS.2009.1801,
author = {Arvind, Vikraman and Mukhopadhyay, Partha},
title = {{Quantum Query Complexity of Multilinear Identity Testing}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {87--98},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1801},
URN = {urn:nbn:de:0030-drops-18014},
doi = {10.4230/LIPIcs.STACS.2009.1801},
annote = {Keywords: Quantum algorithm, Identity testing, Query complexity, Multilinear polynomials}
}
Document
An Order on Sets of Tilings Corresponding to an Order on Languages
Abstract
Traditionally a tiling is defined with a finite number of finite forbidden patterns. We can generalize this notion considering any set of patterns. Generalized tilings defined in this way can be studied with a dynamical point of view, leading to the notion of subshift. In this article we establish a correspondence between an order on subshifts based on dynamical transformations on them and an order on languages of forbidden patterns based on computability properties.
Cite as
Nathalie Aubrun and Mathieu Sablik. An Order on Sets of Tilings Corresponding to an Order on Languages. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 99-110, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{aubrun_et_al:LIPIcs.STACS.2009.1833,
author = {Aubrun, Nathalie and Sablik, Mathieu},
title = {{An Order on Sets of Tilings Corresponding to an Order on Languages}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {99--110},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1833},
URN = {urn:nbn:de:0030-drops-18336},
doi = {10.4230/LIPIcs.STACS.2009.1833},
annote = {Keywords: Tiling, Subshift, Turing machine with oracle, Subdynamics}
}
Document
Compressed Representations of Permutations, and Applications
Abstract
We explore various techniques to compress a permutation $\pi$ over $n$ integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi(i)$ and the application of its inverse $\pi^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $\pi^{k}(i)$ of it, of integer functions, and of inverted lists and suffix arrays.
Cite as
Jeremy Barbay and Gonzalo Navarro. Compressed Representations of Permutations, and Applications. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 111-122, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{barbay_et_al:LIPIcs.STACS.2009.1814,
author = {Barbay, Jeremy and Navarro, Gonzalo},
title = {{Compressed Representations of Permutations, and Applications}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {111--122},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1814},
URN = {urn:nbn:de:0030-drops-18148},
doi = {10.4230/LIPIcs.STACS.2009.1814},
annote = {Keywords: Compression, Permutations, Succinct data structures, Adaptive sorting}
}
Document
On the Average Complexity of Moore's State Minimization Algorithm
Abstract
We prove that, for any arbitrary finite alphabet and for the uniform distribution over deterministic and accessible automata with $n$ states, the average complexity of Moore's state minimization algorithm is in $\mathcal{O}(n \log n)$. Moreover this bound is tight in the case of unary automata.
Cite as
Frederique Bassino, Julien David, and Cyril Nicaud. On the Average Complexity of Moore's State Minimization Algorithm. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 123-134, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{bassino_et_al:LIPIcs.STACS.2009.1822,
author = {Bassino, Frederique and David, Julien and Nicaud, Cyril},
title = {{On the Average Complexity of Moore's State Minimization Algorithm}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {123--134},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1822},
URN = {urn:nbn:de:0030-drops-18222},
doi = {10.4230/LIPIcs.STACS.2009.1822},
annote = {Keywords: Finite automata, State minimization, Moore’s algorithm, Average complexity}
}
Document
Testing Linear-Invariant Non-Linear Properties
Abstract
We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including the linearity test and the test for Reed-Muller codes, has mostly focused on such tasks for linear properties. The one exception is a test due to Green for {}``triangle freeness'': A function $f:\mathbb{F}_{2}^{n}\to\mathbb{F}_{2}$ satisfies this property if $f(x),f(y),f(x+y)$ do not all equal $1$, for any pair $x,y\in\mathbb{F}_{2}^{n}$.
Here we extend this test to a more systematic study of testing for linear-invariant non-linear properties. We consider properties that are described by a single forbidden pattern (and its linear transformations), i.e., a property is given by $k$ points $v_{1},\ldots,v_{k}\in\mathbb{F}_{2}^{k}$ and $f:\mathbb{F}_{2}^{n}\to\mathbb{F}_{2}$ satisfies the property that if for all linear maps $L:\mathbb{F}_{2}^{k}\to\mathbb{F}_{2}^{n}$ it is the case that $f(L(v_{1})),\ldots,f(L(v_{k}))$ do not all equal $1$. We show that this property is testable if the underlying matroid specified by $v_{1},\ldots,v_{k}$ is a graphic matroid. This extends Green's result to an infinite class of new properties.
Our techniques extend those of Green and in particular we establish a link between the notion of {}``1-complexity linear systems'' of Green and Tao, and graphic matroids, to derive the results.
Cite as
Arnab Bhattacharyya, Victor Chen, Madhu Sudan, and Ning Xie. Testing Linear-Invariant Non-Linear Properties. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 135-146, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{bhattacharyya_et_al:LIPIcs.STACS.2009.1823,
author = {Bhattacharyya, Arnab and Chen, Victor and Sudan, Madhu and Xie, Ning},
title = {{Testing Linear-Invariant Non-Linear Properties}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {135--146},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1823},
URN = {urn:nbn:de:0030-drops-18235},
doi = {10.4230/LIPIcs.STACS.2009.1823},
annote = {Keywords: }
}
Document
Kolmogorov Complexity and Solovay Functions
Abstract
Solovay (1975) proved that there exists a computable upper bound~$f$ of the prefix-free Kolmogorov complexity function~$K$ such that $f(x)=K(x)$ for infinitely many~$x$. In this paper, we consider the class of computable functions~$f$ such that $K(x) \leq f(x)+O(1)$ for all~$x$ and $f(x) \leq K(x)+O(1)$ for infinitely many~$x$, which we call Solovay functions. We show that Solovay functions present interesting connections with randomness notions such as Martin-L\"of randomness and K-triviality.
Cite as
Laurent Bienvenu and Rod Downey. Kolmogorov Complexity and Solovay Functions. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 147-158, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{bienvenu_et_al:LIPIcs.STACS.2009.1810,
author = {Bienvenu, Laurent and Downey, Rod},
title = {{Kolmogorov Complexity and Solovay Functions}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {147--158},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1810},
URN = {urn:nbn:de:0030-drops-18107},
doi = {10.4230/LIPIcs.STACS.2009.1810},
annote = {Keywords: Algorithmic randomness, Kolmogorov complexity, K-triviality}
}
Document
Weak MSO with the Unbounding Quantifier
Abstract
A new class of languages of infinite words is introduced, called the \emph{max-regular languages}, extending the class of $\omega$-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter automaton), and in terms of logic (weak monadic second-order logic with a bounding quantifier). Effective translations between the logic and automata are given.
Cite as
Mikolaj Bojanczyk. Weak MSO with the Unbounding Quantifier. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 159-170, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{bojanczyk:LIPIcs.STACS.2009.1834,
author = {Bojanczyk, Mikolaj},
title = {{Weak MSO with the Unbounding Quantifier}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {159--170},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1834},
URN = {urn:nbn:de:0030-drops-18345},
doi = {10.4230/LIPIcs.STACS.2009.1834},
annote = {Keywords: Automata, Monadic second-order logic}
}
Document
Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs
Abstract
We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The schemes run in $O(n \log n)$ time for graphs embedded on both orientable and non-orientable surfaces. This work generalizes the PTAS frameworks of Borradaile, Klein, and Mathieu (2007 and 2006) from planar graphs to bounded-genus graphs: any future problems shown to admit the required structure theorem for planar graphs will similarly extend to bounded-genus graphs.
Cite as
Glencora Borradaile, Erik D. Demaine, and Siamak Tazari. Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 171-182, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{borradaile_et_al:LIPIcs.STACS.2009.1835,
author = {Borradaile, Glencora and Demaine, Erik D. and Tazari, Siamak},
title = {{Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {171--182},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1835},
URN = {urn:nbn:de:0030-drops-18355},
doi = {10.4230/LIPIcs.STACS.2009.1835},
annote = {Keywords: Polynomial-time approximation scheme, Bounded-genus graph, Embedded graph, Steiner tree, Survivable-network design, Subset TSP}
}
Document
A Polynomial Kernel for Multicut in Trees
Abstract
The {\sc Multicut In Trees} problem consists in deciding, given a tree, a set of requests (i.e. paths in the tree) and an integer $k$, whether there exists a set of $k$ edges cutting all the requests. This problem was shown to be FPT by Guo and Niedermeyer (2005). They also provided an exponential kernel. They asked whether this problem has a polynomial kernel. This question was also raised by Fellows (2006).
We show that {\sc Multicut In Trees} has a polynomial kernel.
Cite as
Nicolas Bousquet, Jean Daligault, Stephan Thomasse, and Anders Yeo. A Polynomial Kernel for Multicut in Trees. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 183-194, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{bousquet_et_al:LIPIcs.STACS.2009.1824,
author = {Bousquet, Nicolas and Daligault, Jean and Thomasse, Stephan and Yeo, Anders},
title = {{A Polynomial Kernel for Multicut in Trees}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {183--194},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1824},
URN = {urn:nbn:de:0030-drops-18247},
doi = {10.4230/LIPIcs.STACS.2009.1824},
annote = {Keywords: }
}
Document
On Local Symmetries and Universality in Cellular Automata
Abstract
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically) universal CA, that is CA able to fully simulate any other CA. In this paper, we show that the asymptotic density of universal cellular automata is 1 in several families of CA defined by local symmetries. We extend results reviously established for captive cellular automata in two significant ways. First, our results apply to well-known families of CA (e.g. the family of outer-totalistic CA containing the Game of Life) and, second, we obtain such density results with both increasing number of states and increasing neighbourhood. Moreover, thanks to universality-preserving encodings, we show that the universality problem remains undecidable in some of those families.
Cite as
Laurent Boyer and Guillaume Theyssier. On Local Symmetries and Universality in Cellular Automata. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 195-206, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{boyer_et_al:LIPIcs.STACS.2009.1836,
author = {Boyer, Laurent and Theyssier, Guillaume},
title = {{On Local Symmetries and Universality in Cellular Automata}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {195--206},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1836},
URN = {urn:nbn:de:0030-drops-18369},
doi = {10.4230/LIPIcs.STACS.2009.1836},
annote = {Keywords: Cellular automata, Universality, Asymptotic density}
}
Document
Qualitative Reachability in Stochastic BPA Games
Abstract
We consider a class of infinite-state stochastic games generated by stateless pushdown automata (or, equivalently, 1-exit recursive state machines), where the winning objective is specified by a regular set of target configurations and a qualitative probability constraint `${>}0$' or `${=}1$'. The goal of one player is to maximize the probability of reaching the target set so that the constraint is satisfied, while the other player aims at the opposite. We show that the winner in such games can be determined in $\textbf{NP} \cap \textbf{co-NP}$. Further, we prove that the winning regions for both players are regular, and we design algorithms which compute the associated finite-state automata. Finally, we show that winning strategies can be synthesized effectively.
Cite as
Tomas Brazdil, Vaclav Brozek, Antonin Kucera, and Jan Obdrzalek. Qualitative Reachability in Stochastic BPA Games. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 207-218, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{brazdil_et_al:LIPIcs.STACS.2009.1837,
author = {Brazdil, Tomas and Brozek, Vaclav and Kucera, Antonin and Obdrzalek, Jan},
title = {{Qualitative Reachability in Stochastic BPA Games}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {207--218},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1837},
URN = {urn:nbn:de:0030-drops-18375},
doi = {10.4230/LIPIcs.STACS.2009.1837},
annote = {Keywords: Stochastic games, Reachability, Pushdown automata}
}
Document
Locally Decodable Quantum Codes
Abstract
We study a quantum analogue of locally decodable error-correcting codes. A $q$-query \emph{locally decodable quantum code} encodes $n$ classical bits in an $m$-qubit state, in such a way that each of the encoded bits can be recovered with high probability by a measurement on at most $q$ qubits of the quantum code, even if a constant fraction of its qubits have been corrupted adversarially. We show that such a quantum code can be transformed into a \emph{classical} $q$-query locally decodable code of the same length that can be decoded well on average (albeit with smaller success probability and noise-tolerance). This shows, roughly speaking, that $q$-query quantum codes are not significantly better than $q$-query classical codes, at least for constant or small $q$.
Cite as
Jop Briet and Ronald de Wolf. Locally Decodable Quantum Codes. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 219-230, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{briet_et_al:LIPIcs.STACS.2009.1813,
author = {Briet, Jop and de Wolf, Ronald},
title = {{Locally Decodable Quantum Codes}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {219--230},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1813},
URN = {urn:nbn:de:0030-drops-18134},
doi = {10.4230/LIPIcs.STACS.2009.1813},
annote = {Keywords: Data structures, Locally decodable codes, Quantum computing}
}
Document
Enumerating Homomorphisms
Abstract
The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graph-theoretical structure of the variables and constraints influences the complexity of the problem is intensively studied. Here we study the problem of enumerating all the solutions with polynomial delay from a similar point of view. It turns out that the enumeration problem behaves very differently from the decision version. We give evidence that it is unlikely that a characterization result similar to the decision version can be obtained. Nevertheless, we show nontrivial cases where enumeration can be done with polynomial delay.
Cite as
Andrei A. Bulatov, Victor Dalmau, Martin Grohe, and Daniel Marx. Enumerating Homomorphisms. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 231-242, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{bulatov_et_al:LIPIcs.STACS.2009.1838,
author = {Bulatov, Andrei A. and Dalmau, Victor and Grohe, Martin and Marx, Daniel},
title = {{Enumerating Homomorphisms}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {231--242},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1838},
URN = {urn:nbn:de:0030-drops-18385},
doi = {10.4230/LIPIcs.STACS.2009.1838},
annote = {Keywords: }
}
Document
Hardness and Algorithms for Rainbow Connectivity
Abstract
An edge-colored graph $G$ is {\em rainbow connected} if any two vertices are connected by a path whose edges have distinct colors. The {\em rainbow connectivity} of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected. In addition to being a natural combinatorial problem, the rainbow connectivity problem is motivated by applications in cellular networks. In this paper we give the first proof that computing $rc(G)$ is NP-Hard. In fact, we prove that it is already NP-Complete to decide if $rc(G)=2$, and also that it is NP-Complete to decide whether a given edge-colored (with an unbounded number of colors) graph is rainbow connected. On the positive side, we prove that for every $\epsilon >0$, a connected graph with minimum degree at least $\epsilon n$ has bounded rainbow connectivity, where the bound depends only on $\epsilon$, and the corresponding coloring can be constructed in polynomial time. Additional non-trivial upper bounds, as well as open problems and conjectures are also presented.
Cite as
Sourav Chakraborty, Eldar Fischer, Arie Matsliah, and Raphael Yuster. Hardness and Algorithms for Rainbow Connectivity. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 243-254, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{chakraborty_et_al:LIPIcs.STACS.2009.1811,
author = {Chakraborty, Sourav and Fischer, Eldar and Matsliah, Arie and Yuster, Raphael},
title = {{Hardness and Algorithms for Rainbow Connectivity}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {243--254},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1811},
URN = {urn:nbn:de:0030-drops-18115},
doi = {10.4230/LIPIcs.STACS.2009.1811},
annote = {Keywords: }
}
Document
Nonclairvoyant Speed Scaling for Flow and Energy
Abstract
We study online nonclairvoyant speed scaling to minimize total flow time plus energy. We first consider the traditional model where the power function is $P(s)=s^\alpha$. We give a nonclairvoyant algorithm that is shown to be $O(\alpha^3)$-competitive. We then show an $\Omega( \alpha^{1/3-\epsilon} )$ lower bound on the competitive ratio of any nonclairvoyant algorithm. We also show that there are power functions for which no nonclairvoyant algorithm can be $O(1)$-competitive.
Cite as
Ho-Leung Chan, Jeff Edmonds, Tak-Wah Lam, Lap-Kei Lee, Alberto Marchetti-Spaccamela, and Kirk Pruhs. Nonclairvoyant Speed Scaling for Flow and Energy. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 255-264, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{chan_et_al:LIPIcs.STACS.2009.1815,
author = {Chan, Ho-Leung and Edmonds, Jeff and Lam, Tak-Wah and Lee, Lap-Kei and Marchetti-Spaccamela, Alberto and Pruhs, Kirk},
title = {{Nonclairvoyant Speed Scaling for Flow and Energy}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {255--264},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1815},
URN = {urn:nbn:de:0030-drops-18151},
doi = {10.4230/LIPIcs.STACS.2009.1815},
annote = {Keywords: }
}
Document
An Approximation Algorithm for l_infinity Fitting Robinson Structures to Distances
Abstract
In this paper, we present a factor 16 approximation algorithm for the following NP-hard distance fitting problem: given a finite set $X$ and a distance $d$ on $X$, find a Robinsonian distance $d_R$ on $X$ minimizing the $l_{\infty}$-error $||d-d_R||_{\infty}=\mbox{max}_{x,y\in X}\{ |d(x,y)-d_R(x,y)|\}.$ A distance $d_R$ on a finite set $X$ is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonalalong any row or column. Robinsonian distances generalize ultrametrics, line distances and occur in the seriation problems and in classification.
Cite as
Victor Chepoi and Morgan Seston. An Approximation Algorithm for l_infinity Fitting Robinson Structures to Distances. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 265-276, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{chepoi_et_al:LIPIcs.STACS.2009.1816,
author = {Chepoi, Victor and Seston, Morgan},
title = {{An Approximation Algorithm for l\underlineinfinity Fitting Robinson Structures to Distances}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {265--276},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1816},
URN = {urn:nbn:de:0030-drops-18167},
doi = {10.4230/LIPIcs.STACS.2009.1816},
annote = {Keywords: Robinsonian dissimilarity, Approximation algorithm, Fitting problem}
}
Document
Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties
Abstract
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynomials almost uniformly at random. The statistical distance between the output distribution of the algorithm and the uniform distribution on the set of common zeros is polynomially small in the field size, and the running time of the algorithm is polynomial in the description of the polynomials and their degrees provided that the number of the polynomials is a constant.
Cite as
Mahdi Cheraghchi and Amin Shokrollahi. Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 277-288, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{cheraghchi_et_al:LIPIcs.STACS.2009.1817,
author = {Cheraghchi, Mahdi and Shokrollahi, Amin},
title = {{Almost-Uniform Sampling of Points on High-Dimensional Algebraic Varieties}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {277--288},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1817},
URN = {urn:nbn:de:0030-drops-18174},
doi = {10.4230/LIPIcs.STACS.2009.1817},
annote = {Keywords: Uniform sampling, Algebraic varieties, Randomized algorithms, Computational complexity}
}
Document
Reverse Engineering Prefix Tables
Abstract
The Prefix table of a string reports for each position the maximal length of its prefixes starting here. The Prefix table and its dual Suffix table are basic tools used in the design of the most efficient string-matching and pattern extraction algorithms. These tables can be computed in linear time independently of the alphabet size.
We give an algorithmic characterisation of a Prefix table (it can be adapted to a Suffix table). Namely, the algorithm tests if an integer table of size $n$ is the Prefix table of some word and, if successful, it constructs the lexicographically smallest string having it as a Prefix table. We show that the alphabet of the string can be bounded to $\log_2 n$ letters. The overall algorithm runs in $O(n)$ time.
Cite as
Julien Clement, Maxime Crochemore, and Giuseppina Rindone. Reverse Engineering Prefix Tables. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 289-300, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{clement_et_al:LIPIcs.STACS.2009.1825,
author = {Clement, Julien and Crochemore, Maxime and Rindone, Giuseppina},
title = {{Reverse Engineering Prefix Tables}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {289--300},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1825},
URN = {urn:nbn:de:0030-drops-18258},
doi = {10.4230/LIPIcs.STACS.2009.1825},
annote = {Keywords: Design and analysis of algorithms, Algorithms on strings, Pattern matching, String matching, Combinatorics on words, Prefix table, Suffix table}
}
Document
The Price of Anarchy in Cooperative Network Creation Games
Abstract
We analyze the structure of equilibria and the price of anarchy in the family of network creation games considered extensively in the past few years, which attempt to unify the network design and network routing problems by modeling both creation and usage costs. In general, the games are played on a host graph, where each node is a selfish independent agent (player) and each edge has a fixed link creation cost~$\alpha$. Together the agents create a network (a subgraph of the host graph) while selfishly minimizing the link creation costs plus the sum of the distances to all other players (usage cost). In this paper, we pursue two important facets of the network creation~game.
First, we study extensively a natural version of the game, called the cooperative model, where nodes can collaborate and share the cost of creating any edge in the host graph. We prove the first nontrivial bounds in this model, establishing that the price of anarchy is polylogarithmic in $n$ for all values of~$\alpha$ in complete host graphs. This bound is the first result of this type for any version of the network creation game; most previous general upper bounds are polynomial in~$n$. Interestingly, we also show that equilibrium graphs have polylogarithmic diameter for the most natural range of~$\alpha$ (at most $n \mathop{\rm polylg}\nolimits n$).
Second, we study the impact of the natural assumption that the host graph is a general graph, not necessarily complete. This model is a simple example of nonuniform creation costs among the edges (effectively allowing weights of $\alpha$ and~$\infty$). We prove the first assemblage of upper and lower bounds for this context, establishing nontrivial tight bounds for many ranges of~$\alpha$, for both the unilateral and cooperative versions of network creation. In particular, we establish polynomial lower bounds for both versions and many ranges of~$\alpha$, even for this simple nonuniform cost model, which sharply contrasts the conjectured constant bounds for these games in complete (uniform) graphs.
Cite as
Erik D. Demaine, MohammadTaghi Hajiaghayi, Hamid Mahini, and Morteza Zadimoghaddam. The Price of Anarchy in Cooperative Network Creation Games. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 301-312, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{demaine_et_al:LIPIcs.STACS.2009.1839,
author = {Demaine, Erik D. and Hajiaghayi, MohammadTaghi and Mahini, Hamid and Zadimoghaddam, Morteza},
title = {{The Price of Anarchy in Cooperative Network Creation Games}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {301--312},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1839},
URN = {urn:nbn:de:0030-drops-18390},
doi = {10.4230/LIPIcs.STACS.2009.1839},
annote = {Keywords: }
}
Document
Error-Correcting Data Structures
Abstract
We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been corrupted by a constant fraction of errors. This new model is the common generalization of (static) data structures and locally decodable error-correcting codes. The main issue is the tradeoff between the space used by the data structure and the time (number of probes) needed to answer a query about the encoded object. We prove a number of upper and lower bounds on various natural error-correcting data structure problems. In particular, we show that the optimal length of error-correcting data structures for the {\sc Membership} problem (where we want to store subsets of size $s$ from a universe of size $n$) is closely related to the optimal length of locally decodable codes for $s$-bit strings.
Cite as
Ronald de Wolf. Error-Correcting Data Structures. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 313-324, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{dewolf:LIPIcs.STACS.2009.1802,
author = {de Wolf, Ronald},
title = {{Error-Correcting Data Structures}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {313--324},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1802},
URN = {urn:nbn:de:0030-drops-18024},
doi = {10.4230/LIPIcs.STACS.2009.1802},
annote = {Keywords: Data structures, Error-correcting codes, Locally decodable codes, Membership}
}
Document
Fragments of First-Order Logic over Infinite Words
Abstract
We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic $\mathrm{FO}[<]$ for $\omega$-languages: $\Sigma_2$, $\Delta_2$, $\mathrm{FO}^2 \cap \Sigma_2$ (and by duality $\mathrm{FO}^2 \cap \Pi_2$), and $\mathrm{FO}^2$. These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke (1998) and Boja{\'n}czyk (2008) and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties.
Cite as
Volker Diekert and Manfred Kufleitner. Fragments of First-Order Logic over Infinite Words. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 325-336, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{diekert_et_al:LIPIcs.STACS.2009.1818,
author = {Diekert, Volker and Kufleitner, Manfred},
title = {{Fragments of First-Order Logic over Infinite Words}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {325--336},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1818},
URN = {urn:nbn:de:0030-drops-18185},
doi = {10.4230/LIPIcs.STACS.2009.1818},
annote = {Keywords: Infinite words, Regular languages, First-order logic, Automata theory, Semigroups, Topology}
}
Document
Undecidable Properties of Limit Set Dynamics of Cellular Automata
Abstract
Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial properties of limit sets are undecidable. In this paper we consider properties of limit set dynamics, i.e. properties of the dynamics of Cellular Automata restricted to their limit sets. There can be no equivalent of Kari's Theorem for limit set dynamics. Anyway we show that there is a large class of undecidable properties of limit set dynamics, namely all properties of limit set dynamics which imply stability or the existence of a unique subshift attractor. As a consequence we have that it is undecidable whether the cellular automaton map restricted to the limit set is the identity, closing, injective, expansive, positively expansive, transitive.
Cite as
Pietro Di Lena and Luciano Margara. Undecidable Properties of Limit Set Dynamics of Cellular Automata. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 337-348, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{dilena_et_al:LIPIcs.STACS.2009.1819,
author = {Di Lena, Pietro and Margara, Luciano},
title = {{Undecidable Properties of Limit Set Dynamics of Cellular Automata}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {337--348},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1819},
URN = {urn:nbn:de:0030-drops-18194},
doi = {10.4230/LIPIcs.STACS.2009.1819},
annote = {Keywords: Cellular automata, Undecidability, Symbolic dynamics}
}
Document
Semi-Online Preemptive Scheduling: One Algorithm for All Variants
Abstract
We present a unified optimal semi-online algorithm for preemptive scheduling on uniformly related machines with the objective to minimize the makespan. This algorithm works for all types of semi-online restrictions, including the ones studied before, like sorted (decreasing) jobs, known sum of processing times, known maximal processing time, their combinations, and so on. Based on the analysis of this algorithm, we derive some global relations between various semi-online restrictions and tight bounds on the approximation ratios for a small number of machines.
Cite as
Tomas Ebenlendr and Jiri Sgall. Semi-Online Preemptive Scheduling: One Algorithm for All Variants. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 349-360, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{ebenlendr_et_al:LIPIcs.STACS.2009.1840,
author = {Ebenlendr, Tomas and Sgall, Jiri},
title = {{Semi-Online Preemptive Scheduling: One Algorithm for All Variants}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {349--360},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1840},
URN = {urn:nbn:de:0030-drops-18406},
doi = {10.4230/LIPIcs.STACS.2009.1840},
annote = {Keywords: On-line algorithms, Scheduling}
}
Document
Improved Approximations for Guarding 1.5-Dimensional Terrains
Abstract
We present a 4-approximation algorithm for the problem of placing the fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5 (J. King, 2006). Unlike most of the previous techniques, our method is based on rounding the linear programming relaxation of the corresponding covering problem. Besides the simplicity of the analysis, which mainly relies on decomposing the constraint matrix of the LP into totally balanced matrices, our algorithm, unlike previous work, generalizes to the weighted and partial versions of the basic problem.
Cite as
Khaled Elbassioni, Erik Krohn, Domagoj Matijevic, Julian Mestre, and Domagoj Severdija. Improved Approximations for Guarding 1.5-Dimensional Terrains. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 361-372, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{elbassioni_et_al:LIPIcs.STACS.2009.1841,
author = {Elbassioni, Khaled and Krohn, Erik and Matijevic, Domagoj and Mestre, Julian and Severdija, Domagoj},
title = {{Improved Approximations for Guarding 1.5-Dimensional Terrains}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {361--372},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1841},
URN = {urn:nbn:de:0030-drops-18410},
doi = {10.4230/LIPIcs.STACS.2009.1841},
annote = {Keywords: Covering problems, Guarding 1.5-terrains, Approximation algorithms, Linear programming, Totally balanced matrices}
}
Document
Cover Time and Broadcast Time
Abstract
We introduce a new technique for bounding the cover time of random walks by relating it to the runtime of randomized broadcast. In particular, we strongly confirm for dense graphs the intuition of Chandra et al. (1997) that ``the cover time of the graph is an appropriate metric for the performance of certain kinds of randomized broadcast algorithms''. In more detail, our results are as follows:
\begin{itemize}
\item For any graph $G=(V,E)$ of size $n$ and minimum degree $\delta$, we have $\mathcal{R}(G)= \mathcal{O}(\frac{|E|}{\delta} \cdot \log n)$, where $\mathcal{R}(G)$ denotes the quotient of the cover time and broadcast time. This bound is tight for binary trees and tight up to logarithmic factors for many graphs including hypercubes, expanders and lollipop graphs.
\item For any $\delta$-regular (or almost $\delta$-regular) graph $G$ it holds that $\mathcal{R}(G) = \Omega(\frac{\delta^2}{n} \cdot \frac{1}{\log n})$. Together with our upper bound on $\mathcal{R}(G)$, this lower bound strongly confirms the intuition of Chandra et al.~for graphs with minimum degree $\Theta(n)$, since then the cover time equals the broadcast time multiplied by $n$ (neglecting logarithmic factors).
\item Conversely, for any $\delta$ we construct almost $\delta$-regular graphs that satisfy $\mathcal{R}(G) = \mathcal{O}(\max \{ \sqrt{n},\delta \} \cdot \log^2 n)$. Since any regular expander satisfies $\mathcal{R}(G) = \Theta(n)$, the strong relationship given above does not hold if $\delta$ is polynomially smaller than $n$.
\end{itemize}
Our bounds also demonstrate that the relationship between cover time and broadcast time is much stronger than the known relationships between any of them and the mixing time (or the closely related spectral gap).
Cite as
Robert Elsässer and Thomas Sauerwald. Cover Time and Broadcast Time. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 373-384, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{elsasser_et_al:LIPIcs.STACS.2009.1842,
author = {Els\"{a}sser, Robert and Sauerwald, Thomas},
title = {{Cover Time and Broadcast Time}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {373--384},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1842},
URN = {urn:nbn:de:0030-drops-18421},
doi = {10.4230/LIPIcs.STACS.2009.1842},
annote = {Keywords: Random walk, Randomized algorithms, Parallel and distributed algorithms}
}
Document
Economical Caching
Abstract
We study the management of buffers and storages in environments with unpredictably varying prices in a competitive analysis. In the economical caching problem, there is a storage with a certain capacity. For each time step, an online algorithm is given a price from the interval $[1,\alpha]$, a consumption, and possibly a buying limit. The online algorithm has to decide the amount to purchase from some commodity, knowing the parameter $\alpha$ but without knowing how the price evolves in the future. The algorithm can purchase at most the buying limit. If it purchases more than the current consumption, then the excess is stored in the storage; otherwise, the gap between consumption and purchase must be taken from the storage. The goal is to minimize the total cost. Interesting applications are, for example, stream caching on mobile devices with different classes of service, battery management in micro hybrid cars, and the efficient purchase of resources.
First we consider the simple but natural class of algorithms that can informally be described as memoryless. We show that these algorithms cannot achieve a competitive ratio below $\sqrt{\alpha}$. Then we present a more sophisticated deterministic algorithm achieving a competitive ratio of
\[\textstyle
\frac{1}{W\left(\frac{1-\alpha}{e\alpha}\right)+1} \in
\left[\frac{\sqrt{\alpha}}{\sqrt{2}},
\frac{\sqrt{\alpha}+1}{\sqrt{2}}
\right] \enspace, \]
where $W$ denotes the Lambert~W function. We prove that this algorithm is optimal and that not even randomized online algorithms can achieve a better competitive ratio. On the other hand, we show how to achieve a constant competitive ratio if the storage capacity of the online algorithm exceeds the storage capacity of an optimal offline algorithm by a factor of $\log \alpha$.
Cite as
Matthias Englert, Heiko Röglin, Jacob Spönemann, and Berthold Vöcking. Economical Caching. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 385-396, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{englert_et_al:LIPIcs.STACS.2009.1826,
author = {Englert, Matthias and R\"{o}glin, Heiko and Sp\"{o}nemann, Jacob and V\"{o}cking, Berthold},
title = {{Economical Caching}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {385--396},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1826},
URN = {urn:nbn:de:0030-drops-18263},
doi = {10.4230/LIPIcs.STACS.2009.1826},
annote = {Keywords: Online algorithms, Competitive analysis, Storage management}
}
Document
Computing Graph Roots Without Short Cycles
Abstract
Graph $G$ is the square of graph $H$ if two vertices $x,y$ have an edge in $G$ if and only if $x,y$ are of distance at most two in $H$. Given $H$ it is easy to compute its square $H^2$, however Motwani and Sudan proved that it is NP-complete to determine if a given graph $G$ is the square of some graph $H$ (of girth $3$). In this paper we consider the characterization and recognition problems of graphs that are squares of graphs of small girth, i.e. to determine if $G=H^2$ for some graph $H$ of small girth. The main results are the following.
\begin{itemize}
\item There is a graph theoretical characterization for graphs that are squares of some graph of girth at least $7$. A corollary is that if a graph $G$ has a square root $H$ of girth at least $7$ then $H$ is unique up to isomorphism.
\item There is a polynomial time algorithm to recognize if $G=H^2$ for some graph $H$ of girth at least $6$.
\item It is NP-complete to recognize if $G=H^2$ for some graph $H$ of girth $4$.
\end{itemize}
These results almost provide a dichotomy theorem for the complexity of the recognition problem in terms of girth of the square roots. The algorithmic and graph theoretical results generalize previous results on tree square roots, and provide polynomial time algorithms to compute a graph square root of small girth if it exists. Some open questions and conjectures will also be discussed.
Cite as
Babak Farzad, Lap Chi Lau, Van Bang Le, and Nguyen Ngoc Tuy. Computing Graph Roots Without Short Cycles. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 397-408, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{farzad_et_al:LIPIcs.STACS.2009.1827,
author = {Farzad, Babak and Lau, Lap Chi and Le, Van Bang and Tuy, Nguyen Ngoc},
title = {{Computing Graph Roots Without Short Cycles}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {397--408},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1827},
URN = {urn:nbn:de:0030-drops-18279},
doi = {10.4230/LIPIcs.STACS.2009.1827},
annote = {Keywords: Graph roots, Graph powers, Recognition algorithms, NP-completeness}
}
Document
A Generalization of Nemhauser and Trotter's Local Optimization Theorem
Abstract
The Nemhauser-Trotter local optimization theorem applies to the NP-hard \textsc{Vertex Cover} problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter's result to vertex deletion and graph packing problems, introducing novel algorithmic strategies based on purely combinatorial arguments (not referring to linear programming as the Nemhauser-Trotter result originally did).
We exhibit our framework using a generalization of \textsc{Vertex Cover}, called \textrm{\sc Bounded-Degree Deletion}, that has promise to become an important tool in the analysis of gene and other biological networks. For some fixed~$d\geq 0$, \textrm{\sc Bounded-Degree Deletion} asks to delete as few vertices as possible from a graph in order to transform it into a graph with maximum vertex degree at most~$d$. \textsc{Vertex Cover} is the special case of $d=0$. Our generalization of the Nemhauser-Trotter theorem implies that \textrm{\sc Bounded-Degree Deletion} has a problem kernel with a linear number of vertices for every constant~$d$. We also outline an application of our extremal combinatorial approach to the problem of packing stars with a bounded number of leaves. Finally, charting the border between (parameterized) tractability and intractability for \textrm{\sc Bounded-Degree Deletion}, we provide a W[2]-hardness result for \textrm{\sc Bounded-Degree Deletion} in case of unbounded $d$-values.
Cite as
Michael R. Fellows, Jiong Guo, Hannes Moser, and Rolf Niedermeier. A Generalization of Nemhauser and Trotter's Local Optimization Theorem. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 409-420, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{fellows_et_al:LIPIcs.STACS.2009.1820,
author = {Fellows, Michael R. and Guo, Jiong and Moser, Hannes and Niedermeier, Rolf},
title = {{A Generalization of Nemhauser and Trotter's Local Optimization Theorem}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {409--420},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1820},
URN = {urn:nbn:de:0030-drops-18200},
doi = {10.4230/LIPIcs.STACS.2009.1820},
annote = {Keywords: Algorithms, Computational complexity, NP-hard problems, W\lbrack2\rbrack-completeness, Graph problems, Combinatorial optimization, Fixed-parameter tractability, K}
}
Document
Kernel(s) for Problems with No Kernel: On Out-Trees with Many Leaves
Abstract
The {\sc $k$-Leaf Out-Branching} problem is to find an out-branching, that is a rooted oriented spanning tree, with at least $k$ leaves in a given digraph. The problem has recently received much attention from the viewpoint of parameterized algorithms. Here, we take a kernelization based approach to the {\sc $k$-Leaf-Out-Branching} problem. We give the first polynomial kernel for {\sc Rooted $k$-Leaf-Out-Branching}, a variant of {\sc $k$-Leaf-Out-Branching} where the root of the tree searched for is also a part of the input. Our kernel has cubic size and is obtained using extremal combinatorics.
For the {\sc $k$-Leaf-Out-Branching} problem, we show that no polynomial kernel is possible unless the polynomial hierarchy collapses to third level by applying a recent breakthrough result by Bodlaender et al. (ICALP 2008) in a non-trivial fashion. However, our positive results for {\sc Rooted $k$-Leaf-Out-Branching} immediately imply that the seemingly intractable {\sc $k$-Leaf-Out-Branching} problem admits a data reduction to $n$ independent $O(k^3)$ kernels. These two results, tractability and intractability side by side, are the first ones separating {\it many-to-one kernelization} from {\it Turing kernelization}. This answers affirmatively an open problem regarding ``cheat kernelization'' raised by Mike Fellows and Jiong Guo independently.
Cite as
Henning Fernau, Fedor V. Fomin, Daniel Lokshtanov, Daniel Raible, Saket Saurabh, and Yngve Villanger. Kernel(s) for Problems with No Kernel: On Out-Trees with Many Leaves. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 421-432, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{fernau_et_al:LIPIcs.STACS.2009.1843,
author = {Fernau, Henning and Fomin, Fedor V. and Lokshtanov, Daniel and Raible, Daniel and Saurabh, Saket and Villanger, Yngve},
title = {{Kernel(s) for Problems with No Kernel: On Out-Trees with Many Leaves}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {421--432},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1843},
URN = {urn:nbn:de:0030-drops-18437},
doi = {10.4230/LIPIcs.STACS.2009.1843},
annote = {Keywords: Parameterized algorithms, Kernelization, Out-branching, Max-leaf, Lower bounds}
}
Document
Forward Analysis for WSTS, Part I: Completions
Abstract
Well-structured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the theoretical framework for manipulating downward-closed sets was missing. We answer this problem, using insights from domain theory (dcpos and ideal completions), from topology (sobrifications), and shed new light on the notion of adequate domains of limits.
Cite as
Alain Finkel and Jean Goubault-Larrecq. Forward Analysis for WSTS, Part I: Completions. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 433-444, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{finkel_et_al:LIPIcs.STACS.2009.1844,
author = {Finkel, Alain and Goubault-Larrecq, Jean},
title = {{Forward Analysis for WSTS, Part I: Completions}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {433--444},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1844},
URN = {urn:nbn:de:0030-drops-18444},
doi = {10.4230/LIPIcs.STACS.2009.1844},
annote = {Keywords: WSTS, Forward analysis, Completion, Karp-Miller procedure, Domain theory, Sober spaces, Noetherian spaces}
}
Document
Approximating Acyclicity Parameters of Sparse Hypergraphs
Abstract
The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello (PODS'99, PODS'01) in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx in SODA'06, who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending tractability of many problems in database theory and artificial intelligence. Computing each of these width parameters is known to be an NP-hard problem. Moreover, the (generalized) hypertree width of an n-vertex hypergraph cannot be approximated within a logarithmic factor unless P=NP. In this paper, we study the approximability of (generalized, fractional) hyper treewidth of sparse hypergraphs where the criterion of sparsity reflects the sparsity of their incidence graphs. Our first step is to prove that the (generalized, fractional) hypertree width of a hypergraph is constant-factor sandwiched by the treewidth of its incidence graph, when the incidence graph belongs to some apex-minor-free graph class (the family of apex-minor-free graph classes includes planar graphs and graphs of bounded genus). This determines the combinatorial borderline above which the notion of (generalized, fractional) hypertree width becomes essentially more general than treewidth, justifying that way its functionality as a hypergraph acyclicity measure. While for more general sparse families of hypergraphs treewidth of incidence graphs and all hypertree width parameters may differ arbitrarily, there are sparse families where a constant factor approximation algorithm is possible. In particular, we give a constant factor approximation polynomial time algorithm for (generalized, fractional) hypertree width on hypergraphs whose incidence graphs belong to some H-minor-free graph class. This extends the results of Feige, Hajiaghayi, and Lee from STOC'05 on approximating treewidth of H-minor-free graphs.
Cite as
Fedor V. Fomin, Petr A. Golovach, and Dimitrios M. Thilikos. Approximating Acyclicity Parameters of Sparse Hypergraphs. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 445-456, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{fomin_et_al:LIPIcs.STACS.2009.1803,
author = {Fomin, Fedor V. and Golovach, Petr A. and Thilikos, Dimitrios M.},
title = {{Approximating Acyclicity Parameters of Sparse Hypergraphs}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {445--456},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1803},
URN = {urn:nbn:de:0030-drops-18034},
doi = {10.4230/LIPIcs.STACS.2009.1803},
annote = {Keywords: Graph, Hypergraph, Hypertree width, Treewidth}
}
Document
Optimal Cache-Aware Suffix Selection
Abstract
Given string $S[1..N]$ and integer $k$, the {\em suffix selection} problem is to determine the $k$th lexicographically smallest amongst the suffixes $S[i\ldots N]$, $1 \leq i \leq N$. We study the suffix selection problem in the cache-aware model that captures two-level memory inherent in computing systems, for a \emph{cache} of limited size $M$ and block size $B$. The complexity of interest is the number of block transfers. We present an optimal suffix selection algorithm in the cache-aware model, requiring $\Theta\left(N/B\right)$ block transfers, for any string $S$ over an unbounded alphabet (where characters can only be compared), under the common tall-cache assumption (i.e. $M=\Omega\left(B^{1+\epsilon}\right)$, where $\epsilon<1$). Our algorithm beats the bottleneck bound for permuting an input array to the desired output array, which holds for nearly any nontrivial problem in hierarchical memory models.
Cite as
Gianni Franceschini, Roberto Grossi, and S. Muthukrishnan. Optimal Cache-Aware Suffix Selection. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 457-468, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{franceschini_et_al:LIPIcs.STACS.2009.1845,
author = {Franceschini, Gianni and Grossi, Roberto and Muthukrishnan, S.},
title = {{Optimal Cache-Aware Suffix Selection}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {457--468},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1845},
URN = {urn:nbn:de:0030-drops-18452},
doi = {10.4230/LIPIcs.STACS.2009.1845},
annote = {Keywords: }
}
Document
Randomness on Computable Probability Spaces - A Dynamical Point of View
Abstract
We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a \emph{dynamical} notion of randomness: typicality. Roughly, a point is \emph{typical} for some dynamic, if it follows the statistical behavior of the system (Birkhoff's pointwise ergodic theorem). We prove that a point is Schnorr random if and only if it is typical for every \emph{mixing} computable dynamics. To prove the result we develop some tools for the theory of computable probability spaces (for example, morphisms) that are expected to have other applications.
Cite as
Peter Gacs, Mathieu Hoyrup, and Cristobal Rojas. Randomness on Computable Probability Spaces - A Dynamical Point of View. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 469-480, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{gacs_et_al:LIPIcs.STACS.2009.1828,
author = {Gacs, Peter and Hoyrup, Mathieu and Rojas, Cristobal},
title = {{Randomness on Computable Probability Spaces - A Dynamical Point of View}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {469--480},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1828},
URN = {urn:nbn:de:0030-drops-18280},
doi = {10.4230/LIPIcs.STACS.2009.1828},
annote = {Keywords: Schnorr randomness, Birkhoff's ergodic theorem, Computable measures}
}
Document
The Dynamic Complexity of Formal Languages
Abstract
The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in DynPROP exactly are the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for DynPROP and separates DynPROP from DynQF and DynFO. Further, it is shown that any context-free language can be maintained in DynFO and a number of specific context-free languages, for example all Dyck-languages, are maintainable in DynQF. Furthermore, the dynamic complexity of regular tree languages is investigated and some results concerning arbitrary structures are obtained: there exist first-order definable properties which are not maintainable in DynPROP. On the other hand any existential first-order property can be maintained in DynQF when allowing precomputation.
Cite as
Wouter Gelade, Marcel Marquardt, and Thomas Schwentick. The Dynamic Complexity of Formal Languages. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 481-492, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{gelade_et_al:LIPIcs.STACS.2009.1829,
author = {Gelade, Wouter and Marquardt, Marcel and Schwentick, Thomas},
title = {{The Dynamic Complexity of Formal Languages}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {481--492},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1829},
URN = {urn:nbn:de:0030-drops-18297},
doi = {10.4230/LIPIcs.STACS.2009.1829},
annote = {Keywords: Dynamic complexity, Regular languages, Context-free languages, DynFO}
}
Document
A Complexity Dichotomy for Partition Functions with Mixed Signs
Abstract
\emph{Partition functions}, also known as \emph{homomorphism functions}, form a rich family of graph invariants that contain combinatorial invariants such as the number of $k$-colourings or the number of independent sets of a graph and also the partition functions of certain ``spin glass'' models of statistical physics such as the Ising model.
Building on earlier work by Dyer and Greenhill (2000) and Bulatov and Grohe (2005), we completely classify the computational complexity of partition functions. Our main result is a dichotomy theorem stating that every partition function is either computable in polynomial time or \#P-complete. Partition functions are described by symmetric matrices with real entries, and we prove that it is decidable in polynomial time in terms of the matrix whether a given partition function is in polynomial time or \#P-complete.
While in general it is very complicated to give an explicit algebraic or combinatorial description of the tractable cases, for partition functions described by a Hadamard matrices --- these turn out to be central in our proofs --- we obtain a simple algebraic tractability criterion, which says that the tractable cases are those ``representable'' by a quadratic polynomial over the field $\ensuremath{\mathbb{F}_2}$.
Cite as
Leslie Ann Goldberg, Martin Grohe, Mark Jerrum, and Marc Thurley. A Complexity Dichotomy for Partition Functions with Mixed Signs. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 493-504, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{goldberg_et_al:LIPIcs.STACS.2009.1821,
author = {Goldberg, Leslie Ann and Grohe, Martin and Jerrum, Mark and Thurley, Marc},
title = {{A Complexity Dichotomy for Partition Functions with Mixed Signs}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {493--504},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1821},
URN = {urn:nbn:de:0030-drops-18217},
doi = {10.4230/LIPIcs.STACS.2009.1821},
annote = {Keywords: Computational complexity}
}
Document
Asymptotically Optimal Lower Bounds on the NIH-Multi-Party Information Complexity of the AND-Function and Disjointness
Abstract
Here we prove an asymptotically optimal lower bound on the information complexity of the $k$-party disjointness function with the unique intersection promise, an important special case of the well known disjointness problem, and the AND$_k$-function in the number in the hand model. Our $\Omega(n/k)$ bound for disjointness improves on an earlier $\Omega(n/(k \log k))$ bound by Chakrabarti {\it et al.}~(2003), who obtained an asymptotically tight lower bound for one-way protocols, but failed to do so for the general case. Our result eliminates both the gap between the upper and the lower bound for unrestricted protocols and the gap between the lower bounds for one-way protocols and unrestricted protocols.
Cite as
Andre Gronemeier. Asymptotically Optimal Lower Bounds on the NIH-Multi-Party Information Complexity of the AND-Function and Disjointness. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 505-516, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{gronemeier:LIPIcs.STACS.2009.1846,
author = {Gronemeier, Andre},
title = {{Asymptotically Optimal Lower Bounds on the NIH-Multi-Party Information Complexity of the AND-Function and Disjointness}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {505--516},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1846},
URN = {urn:nbn:de:0030-drops-18465},
doi = {10.4230/LIPIcs.STACS.2009.1846},
annote = {Keywords: Computational complexity, Communication complexity}
}
Document
More Haste, Less Waste: Lowering the Redundancy in Fully Indexable Dictionaries
Abstract
We consider the problem of representing, in a compressed format, a bit-vector~$S$ of $m$ bits with $n$ $\mathbf{1}$s, supporting the following operations, where $b \in \{ \mathbf{0}, \mathbf{1} \}$:
\begin{itemize}
\item $\mathtt{rank}_b(S,i)$ returns the number of occurrences of bit $b$ in the prefix $S\left[1..i\right]$;
\item $\mathtt{select}_b(S,i)$ returns the position of the $i$th occurrence of bit $b$ in $S$.
\end{itemize}
Such a data structure is called \emph{fully indexable dictionary (\textsc{fid})} [Raman, Raman, and Rao, 2007], and is at least as powerful as predecessor data structures. Viewing $S$ as a set $X = \{ x_1, x_2, \ldots, x_n \}$ of $n$ distinct integers drawn from a universe $[m] = \{1, \ldots, m\}$, the predecessor of integer $y \in [m]$ in $X$ is given by $\ensuremath{\mathtt{select}^{}_1}(S, \ensuremath{\mathtt{rank}_1}(S,y-1))$. {\textsc{fid}}s have many applications in succinct and compressed data structures, as they are often involved in the construction of succinct representation for a variety of abstract data types.
Our focus is on space-efficient {\textsc{fid}}s on the \textsc{ram} model with word size $\Theta(\lg m)$ and constant time for all operations, so that the time cost is independent of the input size.
Given the bitstring $S$ to be encoded, having length $m$ and containing $n$ ones, the minimal amount of information that needs to be stored is $B(n,m) = \lceil \log {{m}\choose{n}} \rceil$. The state of the art in building a \textsc{fid}\ for~$S$ is given in~\mbox{}[P\v{a}tra\c{s}cu, 2008] using $B(m,n)+O( m / ( (\log m/ t) ^t) ) + O(m^{3/4}) $ bits, to support the operations in $O(t)$ time.
Here, we propose a parametric data structure exhibiting a time/space trade-off such that, for any real constants $0 < \delta \leq 1/2$, $0 < \varepsilon \leq 1$, and integer $s > 0$, it uses
\[ B(n,m) + O\left(n^{1+\delta} + n \left(\frac{m}{n^s}\right)^\varepsilon\right) \]
bits and performs all the operations in time $O(s\delta^{-1} + \varepsilon^{-1})$. The improvement is twofold: our redundancy can be lowered parametrically and, fixing $s = O(1)$, we get a constant-time \textsc{fid}\ whose space is $B(n,m) + O(m^\varepsilon/\mathrm{poly}(n))$ bits, for sufficiently large $m$. This is a significant improvement compared to the previous bounds for the general case.
Cite as
Roberto Grossi, Alessio Orlandi, Rajeev Raman, and S. Srinivasa Rao. More Haste, Less Waste: Lowering the Redundancy in Fully Indexable Dictionaries. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 517-528, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{grossi_et_al:LIPIcs.STACS.2009.1847,
author = {Grossi, Roberto and Orlandi, Alessio and Raman, Rajeev and Rao, S. Srinivasa},
title = {{More Haste, Less Waste: Lowering the Redundancy in Fully Indexable Dictionaries}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {517--528},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1847},
URN = {urn:nbn:de:0030-drops-18470},
doi = {10.4230/LIPIcs.STACS.2009.1847},
annote = {Keywords: }
}
Document
A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression
Abstract
The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic-programming solution for this problem computes the edit-distance between a pair of strings of total length $O(N)$ in $O(N^2)$ time. To this date, this quadratic upper-bound has never been substantially improved for general strings. However, there are known techniques for breaking this bound in case the strings are known to compress well under a particular compression scheme. The basic idea is to first compress the strings, and then to compute the edit distance between the compressed strings.
As it turns out, practically all known $o(N^2)$ edit-distance algorithms work, in some sense, under the same paradigm described above. It is therefore natural to ask whether there is a single edit-distance algorithm that works for strings which are compressed under any compression scheme. A rephrasing of this question is to ask whether a single algorithm can exploit the compressibility properties of strings under any compression method, even if each string is compressed using a different compression. In this paper we set out to answer this question by using \emph{straight-line programs}. These provide a generic platform for representing many popular compression schemes including the LZ-family, Run-Length Encoding, Byte-Pair Encoding, and dictionary methods.
For two strings of total length $N$ having straight-line program representations of total size $n$, we present an algorithm running in $O(n^{1.4}N^{1.2})$ time for computing the edit-distance of these two strings under any rational scoring function, and an $O(n^{1.34}N^{1.34})$-time algorithm for arbitrary scoring functions. This improves on a recent algorithm of Tiskin that runs in $O(nN^{1.5})$ time, and works only for rational scoring functions.
Cite as
Danny Hermelin, Gad M. Landau, Shir Landau, and Oren Weimann. A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 529-540, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{hermelin_et_al:LIPIcs.STACS.2009.1804,
author = {Hermelin, Danny and Landau, Gad M. and Landau, Shir and Weimann, Oren},
title = {{A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {529--540},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1804},
URN = {urn:nbn:de:0030-drops-18040},
doi = {10.4230/LIPIcs.STACS.2009.1804},
annote = {Keywords: Edit distance, Straight-line Programs, Dynamic programming acceleration via compression, Combinatorial pattern matching}
}
Document
Random Fruits on the Zielonka Tree
Abstract
Stochastic games are a natural model for the synthesis of controllers confronted to adversarial and/or random actions. In particular, $\omega$-regular games of infinite length can represent reactive systems which are not expected to reach a correct state, but rather to handle a continuous stream of events. One critical resource in such applications is the memory used by the controller. In this paper, we study the amount of memory that can be saved through the use of randomisation in strategies, and present matching upper and lower bounds for stochastic Muller games.
Cite as
Florian Horn. Random Fruits on the Zielonka Tree. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 541-552, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{horn:LIPIcs.STACS.2009.1848,
author = {Horn, Florian},
title = {{Random Fruits on the Zielonka Tree}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {541--552},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1848},
URN = {urn:nbn:de:0030-drops-18489},
doi = {10.4230/LIPIcs.STACS.2009.1848},
annote = {Keywords: Model checking, Controller synthesis, Stochastic games, Randomisation}
}
Document
Ambiguity and Communication
Abstract
The ambiguity of a nondeterministic finite automaton (NFA) $N$ for input size $n$ is the maximal number of accepting computations of $N$ for an input of size $n$. For all $k,r \in \mathbb{N}$ we construct languages $L_{r,k}$ which can be recognized by NFA's with size $k \cdot$poly$(r)$ and ambiguity $O(n^k)$, but $L_{r,k}$ has only NFA's with exponential size, if ambiguity $o(n^k)$ is required. In particular, a hierarchy for polynomial ambiguity is obtained, solving a long standing open problem (Ravikumar and Ibarra, 1989, Leung, 1998).
Cite as
Juraj Hromkovic and Georg Schnitger. Ambiguity and Communication. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 553-564, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{hromkovic_et_al:LIPIcs.STACS.2009.1805,
author = {Hromkovic, Juraj and Schnitger, Georg},
title = {{Ambiguity and Communication}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {553--564},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1805},
URN = {urn:nbn:de:0030-drops-18054},
doi = {10.4230/LIPIcs.STACS.2009.1805},
annote = {Keywords: Nondeterministic finite automata, Ambiguity, Communication complexity}
}
Document
On the Borel Inseparability of Game Tree Languages
Abstract
The game tree languages can be viewed as an automata-theoretic counterpart of parity games on graphs. They witness the strictness of the index hierarchy of alternating tree automata, as well as the fixed-point hierarchy over binary trees.
We consider a game tree language of the first non-trivial level, where Eve can force that 0 repeats from some moment on, and its dual, where Adam can force that 1 repeats from some moment on. Both these sets (which amount to one up to an obvious renaming) are complete in the class of co-analytic sets. We show that they cannot be separated by any Borel set, hence {\em a fortiori\/} by any weakly definable set of trees.
This settles a case left open by L. Santocanale and A. Arnold, who have thoroughly investigated the separation property within the $\mu $-calculus and the automata index hierarchies. They showed that separability fails in general for non-deterministic automata of type $\Sigma^{\mu }_{n} $, starting from level $n=3$, while our result settles the missing case $n=2$.
Cite as
Szczepan Hummel, Henryk Michalewski, and Damian Niwinski. On the Borel Inseparability of Game Tree Languages. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 565-576, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{hummel_et_al:LIPIcs.STACS.2009.1849,
author = {Hummel, Szczepan and Michalewski, Henryk and Niwinski, Damian},
title = {{On the Borel Inseparability of Game Tree Languages}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {565--576},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1849},
URN = {urn:nbn:de:0030-drops-18493},
doi = {10.4230/LIPIcs.STACS.2009.1849},
annote = {Keywords: Tree automata, Separation property, Borel sets, Parity games}
}
Document
Equations over Sets of Natural Numbers with Addition Only
Abstract
Systems of equations of the form $X=YZ$ and $X=C$ are considered, in which the unknowns are sets of natural numbers, ``$+$'' denotes pairwise sum of sets $S+T=\ensuremath{ \{ m+n \: | \: m \in S, \; n \in T \} }$, and $C$ is an ultimately periodic constant. It is shown that such systems are computationally universal, in the sense that for every recursive (r.e., co-r.e.) set $S \subseteq \mathbb{N}$ there exists a system with a unique (least, greatest) solution containing a component $T$ with $S=\ensuremath{ \{ n \: | \: 16n+13 \in T \} }$. This implies undecidability of basic properties of these equations. All results also apply to language equations over a one-letter alphabet with concatenation and regular constants.
Cite as
Artur Jez and Alexander Okhotin. Equations over Sets of Natural Numbers with Addition Only. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 577-588, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{jez_et_al:LIPIcs.STACS.2009.1806,
author = {Jez, Artur and Okhotin, Alexander},
title = {{Equations over Sets of Natural Numbers with Addition Only}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {577--588},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1806},
URN = {urn:nbn:de:0030-drops-18061},
doi = {10.4230/LIPIcs.STACS.2009.1806},
annote = {Keywords: }
}
Document
Deciding Unambiguity and Sequentiality of Polynomially Ambiguous Min-Plus Automata
Abstract
This paper solves the unambiguity and the sequentiality problem for polynomially ambiguous min-plus automata. This result is proved through a decidable algebraic characterization involving so-called metatransitions and an application of results from the structure theory of finite semigroups. It is noteworthy that the equivalence problem is known to be undecidable for polynomially ambiguous automata.
Cite as
Daniel Kirsten and Sylvain Lombardy. Deciding Unambiguity and Sequentiality of Polynomially Ambiguous Min-Plus Automata. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 589-600, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{kirsten_et_al:LIPIcs.STACS.2009.1850,
author = {Kirsten, Daniel and Lombardy, Sylvain},
title = {{Deciding Unambiguity and Sequentiality of Polynomially Ambiguous Min-Plus Automata}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {589--600},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1850},
URN = {urn:nbn:de:0030-drops-18509},
doi = {10.4230/LIPIcs.STACS.2009.1850},
annote = {Keywords: Min-plus automata, Determinization, Finite semigroups}
}
Document
Polynomial Kernelizations for MIN F^+Pi_1 and MAX NP
Abstract
The relation of constant-factor approximability to fixed-parameter tractability and kernelization is a long-standing open question. We prove that two large classes of constant-factor approximable problems, namely~$\textsc{MIN F}^+\Pi_1$ and~$\textsc{MAX NP}$, including the well-known subclass~$\textsc{MAX SNP}$, admit polynomial kernelizations for their natural decision versions. This extends results of Cai and Chen (JCSS 1997), stating that the standard parameterizations of problems in~$\textsc{MAX SNP}$ and~$\textsc{MIN F}^+\Pi_1$ are fixed-parameter tractable, and complements recent research on problems that do not admit polynomial kernelizations (Bodlaender et al.\ ICALP 2008).
Cite as
Stefan Kratsch. Polynomial Kernelizations for MIN F^+Pi_1 and MAX NP. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 601-612, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{kratsch:LIPIcs.STACS.2009.1851,
author = {Kratsch, Stefan},
title = {{Polynomial Kernelizations for MIN F^+Pi\underline1 and MAX NP}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {601--612},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1851},
URN = {urn:nbn:de:0030-drops-18511},
doi = {10.4230/LIPIcs.STACS.2009.1851},
annote = {Keywords: Parameterized complexity, Kernelization, Approximation algorithms}
}
Document
Local Multicoloring Algorithms: Computing a Nearly-Optimal TDMA Schedule in Constant Time
Abstract
We are given a set $V$ of autonomous agents (e.g.\ the computers of a distributed system) that are connected to each other by a graph $G=(V,E)$ (e.g.\ by a communication network connecting the agents). Assume that all agents have a unique ID between $1$ and $N$ for a parameter $N\ge|V|$ and that each agent knows its ID as well as the IDs of its neighbors in $G$. Based on this limited information, every agent $v$ must autonomously compute a set of colors $S_v\subseteq C$ such that the color sets $S_u$ and $S_v$ of adjacent agents $u$ and $v$ are disjoint. We prove that there is a deterministic algorithm that uses a total of $|C|=\ensuremath{\mathcal{O}}(\Delta^2\log(N)/\ensuremath{\varepsilon}^2)$ colors such that for every node $v$ of $G$ (i.e., for every agent), we have $|S_v|\ge |C|\cdot(1-\ensuremath{\varepsilon})/(\delta_v+1)$, where $\delta_v$ is the degree of $v$ and where $\Delta$ is the maximum degree of $G$. For $N=\Omega(\Delta^2\log\Delta)$, $\Omega(\Delta^2+\log\log N)$ colors are necessary even to assign at least one color to every node (i.e., to compute a standard vertex coloring). Using randomization, it is possible to assign an $(1-\ensuremath{\varepsilon})/(\delta+1)$-fraction of all colors to every node of degree $\delta$ using only $\ensuremath{\mathcal{O}}(\Delta\log|V|/\ensuremath{\varepsilon}^2)$ colors w.h.p. We show that this is asymptotically almost optimal. For graphs with maximum degree $\Delta=\Omega(\log|V|)$, $\Omega(\Delta\log|V|/\log\log|V|)$ colors are needed in expectation, even to compute a valid coloring.
The described multicoloring problem has direct applications in the context of wireless ad hoc and sensor networks. In order to coordinate the access to the shared wireless medium, the nodes of such a network need to employ some medium access control (MAC) protocol. Typical MAC protocols control the access to the shared channel by time (TDMA), frequency (FDMA), or code division multiple access (CDMA) schemes. Many channel access schemes assign a fixed set of time slots, frequencies, or (orthogonal) codes to the nodes of a network such that nodes that interfere with each other receive disjoint sets of time slots, frequencies, or code sets. Finding a valid assignment of time slots, frequencies, or codes hence directly corresponds to computing a multicoloring of a graph $G$. The scarcity of bandwidth, energy, and computing resources in ad hoc and sensor networks, as well as the often highly dynamic nature of these networks require that the multicoloring can be computed based on as little and as local information as possible.
Cite as
Fabian Kuhn. Local Multicoloring Algorithms: Computing a Nearly-Optimal TDMA Schedule in Constant Time. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 613-624, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{kuhn:LIPIcs.STACS.2009.1852,
author = {Kuhn, Fabian},
title = {{Local Multicoloring Algorithms: Computing a Nearly-Optimal TDMA Schedule in Constant Time}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {613--624},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1852},
URN = {urn:nbn:de:0030-drops-18525},
doi = {10.4230/LIPIcs.STACS.2009.1852},
annote = {Keywords: Distributed algorithms, Graph coloring, Local algorithms, Medium access control, Multicoloring, TDMA, Wireless networks}
}
Document
Efficient Isomorphism Testing for a Class of Group Extensions
Abstract
The group isomorphism problem asks whether two given groups are isomorphic or not. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of isomorphism testing for nonabelian groups. In this paper we study this problem for a class of groups corresponding to one of the simplest ways of constructing nonabelian groups from abelian groups: the groups that are extensions of an abelian group $A$ by a cyclic group $\mathbb{Z}_m$. We present an efficient algorithm solving the group isomorphism problem for all the groups of this class such that the order of $A$ is coprime with $m$. More precisely, our algorithm runs in time almost linear in the orders of the input groups and works in the general setting where the groups are given as black-boxes.
Cite as
Francois Le Gall. Efficient Isomorphism Testing for a Class of Group Extensions. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 625-636, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{legall:LIPIcs.STACS.2009.1830,
author = {Le Gall, Francois},
title = {{Efficient Isomorphism Testing for a Class of Group Extensions}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {625--636},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1830},
URN = {urn:nbn:de:0030-drops-18303},
doi = {10.4230/LIPIcs.STACS.2009.1830},
annote = {Keywords: Polynomial-time algorithms, Group isomorphism, Black-box groups}
}
Document
On Approximating Multi-Criteria TSP
Abstract
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to the approximation ratios obtained for TSP with a single objective function.
We present randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For multi-criteria Max-STSP, where the edge weights have to be symmetric, we devise an algorithm that achieves an approximation ratio of $2/3 - \varepsilon$. For multi-criteria Max-ATSP, where the edge weights may be asymmetric, we present an algorithm with an approximation ratio of $1/2 - \varepsilon$. Our algorithms work for any fixed number $k$ of objectives. To get these ratios, we introduce a decomposition technique for cycle covers. These decompositions are optimal in the sense that no decomposition can always yield more than a fraction of $2/3$ and $1/2$, respectively, of the weight of a cycle cover. Furthermore, we present a deterministic algorithm for bi-criteria Max-STSP\ that achieves an approximation ratio of $61/243 \approx 1/4$.
Finally, we present a randomized approximation algorithm for the asymmetric multi-criteria minimum TSP with triangle inequality (Min-ATSP). This algorithm achieves a ratio of $\log n + \varepsilon$. For this variant of multi-criteria TSP, this is the first approximation algorithm we are aware of. If the distances fulfil the $\gamma$-triangle inequality, its ratio is $1/(1-\gamma) + \varepsilon$.
Cite as
Bodo Manthey. On Approximating Multi-Criteria TSP. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 637-648, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{manthey:LIPIcs.STACS.2009.1853,
author = {Manthey, Bodo},
title = {{On Approximating Multi-Criteria TSP}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {637--648},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1853},
URN = {urn:nbn:de:0030-drops-18537},
doi = {10.4230/LIPIcs.STACS.2009.1853},
annote = {Keywords: Approximation algorithms, Traveling salesman, Multi-criteria optimization}
}
Document
Tractable Structures for Constraint Satisfaction with Truth Tables
Abstract
The way the graph structure of the constraints influences the complexity of constraint satisfaction problems (CSP) is well understood for bounded-arity constraints. The situation is less clear if there is no bound on the arities. In this case the answer depends also on how the constraints are represented in the input. We study this question for the truth table representation of constraints. We introduce a new hypergraph measure {\em adaptive width} and show that CSP with truth tables is polynomial-time solvable if restricted to a class of hypergraphs with bounded adaptive width. Conversely, assuming a conjecture on the complexity of binary CSP, there is no other polynomial-time solvable case.
Cite as
Daniel Marx. Tractable Structures for Constraint Satisfaction with Truth Tables. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 649-660, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{marx:LIPIcs.STACS.2009.1807,
author = {Marx, Daniel},
title = {{Tractable Structures for Constraint Satisfaction with Truth Tables}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {649--660},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1807},
URN = {urn:nbn:de:0030-drops-18079},
doi = {10.4230/LIPIcs.STACS.2009.1807},
annote = {Keywords: Computational complexity, Constraint satisfaction, Treewidth, Adaptive width}
}
Document
Büchi Complementation Made Tight
Abstract
The precise complexity of complementing B\"uchi\ automata is an intriguing and long standing problem. While optimal complementation techniques for finite automata are simple -- it suffices to determinize them using a simple subset construction and to dualize the acceptance condition of the resulting automaton -- B\"uchi\ complementation is more involved. Indeed, the construction of an EXPTIME complementation procedure took a quarter of a century from the introduction of B\"uchi\ automata in the early $60$s, and stepwise narrowing the gap between the upper and lower bound to a simple exponent (of $(6e)^n$ for B\"uchi\ automata with $n$ states) took four decades. While the distance between the known upper ($O\big((0.96\,n)^n\big)$) and lower ($\Omega\big((0.76\,n)^n\big)$) bound on the required number of states has meanwhile been significantly reduced, an exponential factor remains between them. Also, the upper bound on the size of the complement automaton is not linear in the bound of its state space. These gaps are unsatisfactory from a theoretical point of view, but also because B\"uchi\ complementation is a useful tool in formal verification, in particular for the language containment problem. This paper proposes a B\"uchi\ complementation algorithm whose complexity meets, modulo a quadratic ($O(n^2)$) factor, the known lower bound for B\"uchi\ complementation. It thus improves over previous constructions by an exponential factor and concludes the quest for optimal B\"uchi\ complementation algorithms.
Cite as
Sven Schewe. Büchi Complementation Made Tight. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 661-672, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{schewe:LIPIcs.STACS.2009.1854,
author = {Schewe, Sven},
title = {{B\"{u}chi Complementation Made Tight}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {661--672},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1854},
URN = {urn:nbn:de:0030-drops-18543},
doi = {10.4230/LIPIcs.STACS.2009.1854},
annote = {Keywords: Automata and formal languages, Buchi complementation, Automata theory, Nondeterministic Buchi automata}
}
Document
Strong Completeness of Coalgebraic Modal Logics
Abstract
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics often present subtle difficulties - up to the point that canonical models may fail to exist, as is the case e.g. in most probabilistic logics. Here, we present a generic canonical model construction in the semantic framework of coalgebraic modal logic, which pinpoints coherence conditions between syntax and semantics of modal logics that guarantee strong completeness. We apply this method to reconstruct canonical model theorems that are either known or folklore, and moreover instantiate our method to obtain new strong completeness results. In particular, we prove strong completeness of graded modal logic with finite multiplicities, and of the modal logic of exact probabilities.
Cite as
Lutz Schröder and Dirk Pattinson. Strong Completeness of Coalgebraic Modal Logics. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 673-684, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{schroder_et_al:LIPIcs.STACS.2009.1855,
author = {Schr\"{o}der, Lutz and Pattinson, Dirk},
title = {{Strong Completeness of Coalgebraic Modal Logics}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {673--684},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1855},
URN = {urn:nbn:de:0030-drops-18559},
doi = {10.4230/LIPIcs.STACS.2009.1855},
annote = {Keywords: Logic in computer science, Semantics, Deduction, Modal logic, Coalgebra}
}
Document
A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints
Abstract
We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan (1995) and the theory of stable set polytope. We apply it to majority functions and prove their formula size lower bounds improved from the classical result of Khrapchenko (1971). Moreover, we introduce a notion of unbalanced recursive ternary majority functions motivated by a decomposition theory of monotone self-dual functions and give integrally matching upper and lower bounds of their formula size. We also show monotone formula size lower bounds of balanced recursive ternary majority functions improved from the quantum adversary bound of Laplante, Lee and Szegedy (2006).
Cite as
Kenya Ueno. A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 685-696, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{ueno:LIPIcs.STACS.2009.1808,
author = {Ueno, Kenya},
title = {{A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {685--696},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1808},
URN = {urn:nbn:de:0030-drops-18080},
doi = {10.4230/LIPIcs.STACS.2009.1808},
annote = {Keywords: Computational and structural complexity}
}
Document
Extracting the Kolmogorov Complexity of Strings and Sequences from Sources with Limited Independence
Abstract
An infinite binary sequence has randomness rate at least $\sigma$ if, for almost every $n$, the Kolmogorov complexity of its prefix of length $n$ is at least $\sigma n$. It is known that for every rational $\sigma \in (0,1)$, on one hand, there exists sequences with randomness rate $\sigma$ that can not be effectively transformed into a sequence with randomness rate higher than $\sigma$ and, on the other hand, any two independent sequences with randomness rate $\sigma$ can be transformed into a sequence with randomness rate higher than $\sigma$. We show that the latter result holds even if the two input sequences have linear dependency (which, informally speaking, means that all prefixes of length $n$ of the two sequences have in common a constant fraction of their information). The similar problem is studied for finite strings. It is shown that from any two strings with sufficiently large Kolmogorov complexity and sufficiently small dependence, one can effectively construct a string that is random even conditioned by any one of the input strings.
Cite as
Marius Zimand. Extracting the Kolmogorov Complexity of Strings and Sequences from Sources with Limited Independence. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 697-708, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{zimand:LIPIcs.STACS.2009.1812,
author = {Zimand, Marius},
title = {{Extracting the Kolmogorov Complexity of Strings and Sequences from Sources with Limited Independence}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {697--708},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Albers, Susanne and Marion, Jean-Yves},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1812},
URN = {urn:nbn:de:0030-drops-18128},
doi = {10.4230/LIPIcs.STACS.2009.1812},
annote = {Keywords: Algorithmic information theory, Computational complexity, Kolmogorov complexity, Randomness extractors}
}