Volume
LIPIcs, Volume 1
25th 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 2008, February 21-23, 2008, Bordeaux, FranceEditors
Publication Details
- published at: 2008-02-05
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-939897-06-4
- DBLP: db/conf/stacs/stacs2008
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Complete Volume
LIPIcs, Volume 1, STACS'08, Complete Volume
Abstract
LIPIcs, Volume 1, STACS'08, Complete Volume
Cite as
25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@Proceedings{albers_et_al:LIPIcs.STACS.2008,
title = {{LIPIcs, Volume 1, STACS'08, Complete Volume}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2013},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008},
URN = {urn:nbn:de:0030-drops-40958},
doi = {10.4230/LIPIcs.STACS.2008},
annote = {Keywords: LIPIcs, Volume 1, STACS'08, Complete Volume}
}
Document
Front Matter
Abstracts Collection -- 25th International Symposium on Theoretical Aspects of Computer Science
Abstract
The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately
in France and in Germany. The conference of February 21-23, 2008, held in Bordeaux,
is the 25th in this series. Previous meetings took place in Paris (1984), Saarbr\"{u}cken (1985),
Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg
(1991), Cachan (1992), W\"{u}rzburg 1993), Caen (1994), M\"{u}nchen (1995), Grenoble (1996),
L\"{u}beck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002),
Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006) and Aachen (2007).
Cite as
25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. i-xxviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{albers_et_al:LIPIcs.STACS.2008.1378,
author = {Albers, Susanne and Weil, Pascal},
title = {{Abstracts Collection -- 25th International Symposium on Theoretical Aspects of Computer Science}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {i--xxviii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1378},
URN = {urn:nbn:de:0030-drops-13780},
doi = {10.4230/LIPIcs.STACS.2008.1378},
annote = {Keywords: Symposium, theoretical computer science, algorithms and data structures, automata and formal languages, computational and structural complexity, logic in computer science, applications}
}
Document
Preface -- 25th 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
2008 call for papers led to approximately 200 submissions from 38 countries. Each was
assigned to at least three program committee members. The program committee held a
2-week long electronic meeting at the end of November, to select 54 papers. As co-chairs
of this committee, we would like to sincerely thank its members and the many external
referees for the valuable work they put into the reviewing process. The overall very high
quality of the papers that were submitted to the conference made this selection a difficult task.
We would like to express our thanks to the three invited speakers, Maxime Crochemore,
Thomas Schwentick and Mihalis Yannakakis, for their contributions to the proceedings.
Special thanks are due to A. Voronkov for his EasyChair software (www.easychair.org)
which gives the organisers of conferences such as STACS a remarkable level of comfort;
to Ralf Klasing for helping us explore the many possibilities of this brilliant software; to
Emilka Bojanczyk for the design of the STACS poster, proceedings and logo; and to the
members of the Organizing Committee, chaired by David Janin.
An innovation in this year's STACS is the electronic format of the publication. A
printed version was also available at the conference, with ISBN 978-3-939897-06-4. 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 (see www.stacs-conf.org/faq.html
for more details).
Cite as
Susanne Albers and Pascal Weil. Preface -- 25th International Symposium on Theoretical Aspects of Computer Science. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{albers_et_al:LIPIcs.STACS.2008.1326,
author = {Albers, Susanne and Weil, Pascal},
title = {{Preface -- 25th International Symposium on Theoretical Aspects of Computer Science}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {1--10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1326},
URN = {urn:nbn:de:0030-drops-13263},
doi = {10.4230/LIPIcs.STACS.2008.1326},
annote = {Keywords: Symposium, theoretical computer science, algorithms and data structures, automata and formal languages, computational and structural complexity, logic in computer science, applications}
}
Document
Understanding Maximal Repetitions in Strings
Abstract
The cornerstone of any algorithm computing all repetitions in a
string of length $n$ in ${mathcal O(n)$ time is the fact that
the number of runs (or maximal repetitions) is ${mathcal O(n)$.
We give a simple proof of this result. As a consequence of our
approach, the stronger result concerning the linearity of the sum
of exponents of all runs follows easily.
Cite as
Maxime Crochemore and Lucian Ilie. Understanding Maximal Repetitions in Strings. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 11-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{crochemore_et_al:LIPIcs.STACS.2008.1344,
author = {Crochemore, Maxime and Ilie, Lucian},
title = {{Understanding Maximal Repetitions in Strings}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {11--16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1344},
URN = {urn:nbn:de:0030-drops-13442},
doi = {10.4230/LIPIcs.STACS.2008.1344},
annote = {Keywords: Combinatorics on words, repetitions in strings, runs, maximal repetitions, maximal periodicities, sum of exponents}
}
Document
Abstract
A Little Bit Infinite? On Adding Data to Finitely Labelled Structures (Abstract)
Abstract
Finite or infinite strings or trees with labels from a finite alphabet play an important role
in computer science. They can be used to model many interesting objects including system
runs in Automated Verification and XML documents in Database Theory. They allow the
application of formal tools like logical formulas to specify properties and automata for their
implementation. In this framework, many reasoning tasks that are undecidable for general
computational models can be solved algorithmically, sometimes even efficiently.
Nevertheless, the use of finitely labelled structures usually requires an early abstraction
from the real data. For example, theoretical research on XML processing very often con-
centrates on the document structure (including labels) but ignores attribute or text values.
While this abstraction has led to many interesting results, some aspects like key or other
integrity constraints can not be adequately handled.
In Automated Verification of software systems or communication protocols, infinite
domains occur even more naturally, e.g., induced by program data, recursion, time, com-
munication or by unbounded numbers of concurrent processes. Usually one approximates
infinite domains by finite ones in a very early abstraction step.
An alternative approach that has been investigated in recent years is to extend strings
and trees by (a limited amount of) data and to use logical languages with a restricted ex-
pressive power concerning this data. As an example, in the most simple setting, formulas
can only test equality of data values. The driving goal is to identify logical languages and
corresponding automata models which are strong enough to describe interesting proper-
ties of data-enhanced structures while keeping decidability or even feasibility of automatic
reasoning.
The talk gives a basic introduction into data-enhanced finitely labelled structures,
presents examples of their use, and highlights recent decidability and complexity results.
Cite as
Thomas Schwentick. A Little Bit Infinite? On Adding Data to Finitely Labelled Structures (Abstract). In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 17-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{schwentick:LIPIcs.STACS.2008.1325,
author = {Schwentick, Thomas},
title = {{A Little Bit Infinite? On Adding Data to Finitely Labelled Structures}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {17--18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1325},
URN = {urn:nbn:de:0030-drops-13253},
doi = {10.4230/LIPIcs.STACS.2008.1325},
annote = {Keywords: }
}
Document
Equilibria, Fixed Points, and Complexity Classes
Abstract
Many models from a variety of areas involve the computation of an
equilibrium or fixed point of some kind. Examples include Nash
equilibria in games; market equilibria; computing optimal strategies
and the values of competitive games (stochastic and other games);
stable configurations of neural networks; analysing basic stochastic
models for evolution like branching processes and for language like
stochastic context-free grammars; and models that incorporate the
basic primitives of probability and recursion like recursive Markov
chains. It is not known whether these problems can be solved in
polynomial time. There are certain common computational principles
underlying different types of equilibria, which are captured by the
complexity classes PLS, PPAD, and FIXP. Representative complete
problems for these classes are respectively, pure Nash equilibria in
games where they are guaranteed to exist, (mixed) Nash equilibria in
2-player normal form games, and (mixed) Nash equilibria in normal
form games with 3 (or more) players. This paper reviews the
underlying computational principles and the corresponding classes.
Cite as
Mihalis Yannakakis. Equilibria, Fixed Points, and Complexity Classes. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 19-38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{yannakakis:LIPIcs.STACS.2008.1311,
author = {Yannakakis, Mihalis},
title = {{Equilibria, Fixed Points, and Complexity Classes}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {19--38},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1311},
URN = {urn:nbn:de:0030-drops-13110},
doi = {10.4230/LIPIcs.STACS.2008.1311},
annote = {Keywords: Equilibria, Fixed points, Computational Complexity, Game Theory}
}
Document
Pushdown Compression
Abstract
The pressing need for efficient compression schemes for XML
documents has recently been focused on stack computation (Hariharan
and Shankar 2006, League and Eng 2007), and in particular calls for
a formulation of information-lossless stack or pushdown compressors
that allows a formal analysis of their performance and a more
ambitious use of the stack in XML compression, where so far it is
mainly connected to parsing mechanisms. In this paper we introduce
the model of pushdown compressor, based on pushdown transducers
that compute a single injective function while keeping the widest
generality regarding stack computation.
The celebrated Lempel-Ziv algorithm LZ78 was introduced as a general
purpose compression algorithm that outperforms finite-state
compressors on all sequences. We compare the performance of the
Lempel-Ziv algorithm with that of the pushdown compressors, or
compression algorithms that can be implemented with a pushdown
transducer. This comparison is made without any a priori assumption
on the data's source and considering the asymptotic compression
ratio for infinite sequences. We prove that Lempel-Ziv is
incomparable with pushdown compressors.
Cite as
Pilar Albert, Elvira Mayordomo, Philip Moser, and Sylvain Perifel. Pushdown Compression. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 39-48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{albert_et_al:LIPIcs.STACS.2008.1332,
author = {Albert, Pilar and Mayordomo, Elvira and Moser, Philip and Perifel, Sylvain},
title = {{Pushdown Compression}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {39--48},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1332},
URN = {urn:nbn:de:0030-drops-13327},
doi = {10.4230/LIPIcs.STACS.2008.1332},
annote = {Keywords: Finite-state compression, Lempel-Ziv algorithm, pumping-lemma, pushdown compression, XML document}
}
Document
Quantum search with variable times
Abstract
Since Grover's seminal work, quantum search has been studied in
great detail. In the usual search problem, we have a collection of
$n$ items $x_1, ldots, x_n$ and we would like to find $i: x_i=1$.
We consider a new variant of this problem in which evaluating $x_i$
for different $i$ may take a different number of time steps.
Let $t_i$ be the number of time steps required to evaluate $x_i$.
If the numbers $t_i$ are known in advance, we give an algorithm
that solves the problem in $O(sqrt{t_1^2+t_2^2+ldots+t_n^2)$
steps. This is optimal, as we also show a matching lower bound.
The case, when $t_i$ are not known in advance, can be solved with a
polylogarithmic overhead. We also give an application of our new
search algorithm to computing read-once functions.
Cite as
Andris Ambainis. Quantum search with variable times. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 49-60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{ambainis:LIPIcs.STACS.2008.1333,
author = {Ambainis, Andris},
title = {{Quantum search with variable times}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {49--60},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1333},
URN = {urn:nbn:de:0030-drops-13333},
doi = {10.4230/LIPIcs.STACS.2008.1333},
annote = {Keywords: }
}
Document
Structural aspects of tilings
Abstract
In this paper, we study the structure of the set of tilings
produced by any given tile-set. For better understanding this
structure, we address the set of finite patterns that each tiling
contains.
This set of patterns can be analyzed in two different contexts:
the first one is combinatorial and the other topological. These
two approaches have independent merits and, once combined, provide
somehow surprising results.
The particular case where the set of produced tilings is countable
is deeply investigated while we prove that the uncountable case
may have a completely different structure.
We introduce a pattern preorder and also make use of
Cantor-Bendixson rank. Our first main result is that a tile-set
that produces only periodic tilings produces only a finite number
of them. Our second main result exhibits a tiling with exactly
one vector of periodicity in the countable case.
Cite as
Alexis Ballier, Bruno Durand, and Emmanuel Jeandal. Structural aspects of tilings. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 61-72, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{ballier_et_al:LIPIcs.STACS.2008.1334,
author = {Ballier, Alexis and Durand, Bruno and Jeandal, Emmanuel},
title = {{Structural aspects of tilings}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {61--72},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1334},
URN = {urn:nbn:de:0030-drops-13343},
doi = {10.4230/LIPIcs.STACS.2008.1334},
annote = {Keywords: Tiling, domino, patterns, tiling preorder, tiling structure}
}
Document
Limit complexities revisited
Abstract
The main goal of this paper is to put some known results in a
common perspective and to simplify their proofs.
We start with a simple proof of a result from (Vereshchagin, 2002)
saying that $limsup_{nKS(x|n)$ (here $KS(x|n)$ is conditional
(plain) Kolmogorov complexity of $x$ when $n$ is known) equals
$KS^{mathbf{0'(x)$, the plain Kolmogorov complexity with
$mathbf{0'$-oracle.
Then we use the same argument to prove similar results for prefix
complexity (and also improve results of (Muchnik, 1987) about limit
frequencies), a priori probability on binary tree and measure of
effectively open sets. As a by-product, we get a criterion of
$mathbf{0'$ Martin-L"of randomness (called also $2$-randomness)
proved in (Miller, 2004): a sequence $omega$ is $2$-random if and
only if there exists $c$ such that any prefix $x$ of $omega$ is a
prefix of some string $y$ such that $KS(y)ge |y|-c$. (In the
1960ies this property was suggested in (Kolmogorov, 1968) as one of
possible randomness definitions; its equivalence to $2$-randomness
was shown in (Miller, 2004) while proving another $2$-randomness
criterion (see also (Nies et al. 2005)): $omega$ is $2$-random if
and only if $KS(x)ge |x|-c$ for some $c$ and infinitely many
prefixes $x$ of $omega$.
Finally, we show that the low-basis theorem can be used to get
alternative proofs for these results and to improve the result
about effectively open sets; this stronger version implies the
$2$-randomness criterion mentioned in the previous sentence.
Cite as
Laurent Bienvenu, Andrej Muchnik, Alexander Shen, and Nikolay Veraschagin. Limit complexities revisited. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 73-84, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{bienvenu_et_al:LIPIcs.STACS.2008.1335,
author = {Bienvenu, Laurent and Muchnik, Andrej and Shen, Alexander and Veraschagin, Nikolay},
title = {{Limit complexities revisited}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {73--84},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1335},
URN = {urn:nbn:de:0030-drops-13350},
doi = {10.4230/LIPIcs.STACS.2008.1335},
annote = {Keywords: Kolmogorov complexity, limit complexities, limit frequencies, 2-randomness, low basis}
}
Document
Trimmed Moebius Inversion and Graphs of Bounded Degree
Abstract
We study ways to expedite Yates's algorithm for computing the zeta
and Moebius transforms of a function defined on the subset lattice.
We develop a trimmed variant of Moebius inversion that proceeds
point by point, finishing the calculation at a subset before
considering its supersets. For an $n$-element universe $U$ and a
family $scr F$ of its subsets, trimmed Moebius inversion allows us
to compute the number of packings, coverings, and partitions of $U$
with $k$ sets from $scr F$ in time within a polynomial factor (in
$n$) of the number of supersets of the members of $scr F$.
Relying on an intersection theorem of Chung et al. (1986) to bound
the sizes of set families, we apply these ideas to well-studied
combinatorial optimisation problems on graphs of maximum degree
$Delta$. In particular, we show how to compute the Domatic Number
in time within a polynomial factor of
$(2^{Delta+1-2)^{n/(Delta+1)$ and the Chromatic Number in time
within a polynomial factor of
$(2^{Delta+1-Delta-1)^{n/(Delta+1)$. For any constant $Delta$,
these bounds are $O bigl((2-epsilon)^n bigr)$ for $epsilon>0$
independent of the number of vertices $n$.
Cite as
Andreas Björklund, Thore Husfeldt, Petteri Kaski, and Mikko Koivisto. Trimmed Moebius Inversion and Graphs of Bounded Degree. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 85-96, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{bjorklund_et_al:LIPIcs.STACS.2008.1336,
author = {Bj\"{o}rklund, Andreas and Husfeldt, Thore and Kaski, Petteri and Koivisto, Mikko},
title = {{Trimmed Moebius Inversion and Graphs of Bounded Degree}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {85--96},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1336},
URN = {urn:nbn:de:0030-drops-13369},
doi = {10.4230/LIPIcs.STACS.2008.1336},
annote = {Keywords: }
}
Document
On the Complexity of the Interlace Polynomial
Abstract
We consider the two-variable interlace polynomial introduced by
Arratia, Bollob`as and Sorkin (2004). We develop two graph
transformations which allow us to derive point-to-point reductions
for the interlace polynomial. Exploiting these reductions we
obtain new results concerning the computational complexity of
evaluating the interlace polynomial at a fixed point. Regarding
exact evaluation, we prove that the interlace polynomial is #P-hard
to evaluate at every point of the plane, except at one line, where
it is trivially polynomial time computable, and four lines and two
points, where the complexity mostly is still open. This solves a
problem posed by Arratia, Bollob`as and Sorkin (2004). In
particular, we observe that three specializations of the
two-variable interlace polynomial, the vertex-nullity interlace
polynomial, the vertex-rank interlace polynomial and the
independent set polynomial, are almost everywhere #P-hard to
evaluate, too. For the independent set polynomial, our reductions
allow us to prove that it is even hard to approximate at every
point except at $-1$ and~$0$.
Cite as
Markus Bläser and Christian Hoffmann. On the Complexity of the Interlace Polynomial. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 97-108, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{blaser_et_al:LIPIcs.STACS.2008.1337,
author = {Bl\"{a}ser, Markus and Hoffmann, Christian},
title = {{On the Complexity of the Interlace Polynomial}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {97--108},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1337},
URN = {urn:nbn:de:0030-drops-13378},
doi = {10.4230/LIPIcs.STACS.2008.1337},
annote = {Keywords: Computational complexity, approximation, interlace polynomial, independent set polynomial, graph transformation}
}
Document
Minimizing Flow Time in the Wireless Gathering Problem
Abstract
We address the problem of efficient data gathering in a wireless
network through multi-hop communication. We focus on the objective
of minimizing the maximum flow time of a data packet. We prove
that no polynomial time algorithm for this problem can have
approximation ratio less than $Omega(m^{1/3)$ when $m$ packets
have to be transmitted, unless $P = NP$. We then use resource
augmentation to assess the performance of a FIFO-like strategy. We
prove that this strategy is 5-speed optimal, i.e., its cost remains
within the optimal cost if we allow the algorithm to transmit data
at a speed 5 times higher than that of the optimal solution we
compare to.
Cite as
Vincenzo Bonifaci, Peter Korteweg, Alberto Marchetti-Spaccamela, and Leen Stougie. Minimizing Flow Time in the Wireless Gathering Problem. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 109-120, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{bonifaci_et_al:LIPIcs.STACS.2008.1338,
author = {Bonifaci, Vincenzo and Korteweg, Peter and Marchetti-Spaccamela, Alberto and Stougie, Leen},
title = {{Minimizing Flow Time in the Wireless Gathering Problem}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {109--120},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1338},
URN = {urn:nbn:de:0030-drops-13381},
doi = {10.4230/LIPIcs.STACS.2008.1338},
annote = {Keywords: Wireless networks, data gathering, approximation algorithms, distributed algorithms}
}
Document
On Termination for Faulty Channel Machines
Abstract
A channel machine consists of a finite controller together with
several fifo channels; the controller can read messages from the
head of a channel and write messages to the tail of a channel. In
this paper, we focus on channel machines with insertion errors,
i.e., machines in whose channels messages can spontaneously appear.
Such devices have been previously introduced in the study of Metric
Temporal Logic. We consider the termination problem: are all the
computations of a given insertion channel machine finite? We show
that this problem has non-elementary, yet primitive recursive
complexity.
Cite as
Patricia Bouyer, Nicolas Markey, Joël Ouaknine, Philippe Schnoebelen, and James Worrell. On Termination for Faulty Channel Machines. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 121-132, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{bouyer_et_al:LIPIcs.STACS.2008.1339,
author = {Bouyer, Patricia and Markey, Nicolas and Ouaknine, Jo\"{e}l and Schnoebelen, Philippe and Worrell, James},
title = {{On Termination for Faulty Channel Machines}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {121--132},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1339},
URN = {urn:nbn:de:0030-drops-13390},
doi = {10.4230/LIPIcs.STACS.2008.1339},
annote = {Keywords: Automated Verification, Computational Complexity}
}
Document
Stackelberg Network Pricing Games
Abstract
We study a multi-player one-round game termed Stackelberg Network
Pricing Game, in which a leader can set prices for a subset of $m$
priceable edges in a graph. The other edges have a fixed cost.
Based on the leader's decision one or more followers optimize a
polynomial-time solvable combinatorial minimization problem and
choose a minimum cost solution satisfying their requirements based
on the fixed costs and the leader's prices. The leader receives as
revenue the total amount of prices paid by the followers for
priceable edges in their solutions, and the problem is to find
revenue maximizing prices. Our model extends several known pricing
problems, including single-minded and unit-demand pricing, as well
as Stackelberg pricing for certain follower problems like shortest
path or minimum spanning tree. Our first main result is a tight
analysis of a single-price algorithm for the single follower game,
which provides a $(1+varepsilon) log m$-approximation for any
$varepsilon >0$. This can be extended to provide a
$(1+varepsilon )(log k + log m)$-approximation for the general
problem and $k$ followers. The latter result is essentially best
possible, as the problem is shown to be hard to approximate within
$mathcal{O(log^varepsilon k + log^varepsilon m)$. If
followers have demands, the single-price algorithm provides a
$(1+varepsilon )m^2$-approximation, and the problem is hard to
approximate within $mathcal{O(m^varepsilon)$ for some
$varepsilon >0$. Our second main result is a polynomial time
algorithm for revenue maximization in the special case of
Stackelberg bipartite vertex cover, which is based on non-trivial
max-flow and LP-duality techniques. Our results can be extended to
provide constant-factor approximations for any constant number of
followers.
Cite as
Patrick Briest, Martin Hoefer, and Piotr Krysta. Stackelberg Network Pricing Games. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 133-142, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{briest_et_al:LIPIcs.STACS.2008.1340,
author = {Briest, Patrick and Hoefer, Martin and Krysta, Piotr},
title = {{Stackelberg Network Pricing Games}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {133--142},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1340},
URN = {urn:nbn:de:0030-drops-13406},
doi = {10.4230/LIPIcs.STACS.2008.1340},
annote = {Keywords: Stackelberg Games, Algorithmic Pricing, Approximation Algorithms, Inapproximability.}
}
Document
Sublinear Communication Protocols for Multi-Party Pointer Jumping and a Related Lower Bound
Abstract
We study the one-way number-on-the-forehead (NOF) communication
complexity of the $k$-layer pointer jumping problem with $n$
vertices per layer. This classic problem, which has connections to
many aspects of complexity theory, has seen a recent burst of
research activity, seemingly preparing the ground for an
$Omega(n)$ lower bound, for constant $k$. Our first result is a
surprising sublinear --- i.e., $o(n)$ --- upper bound for the
problem that holds for $k ge 3$, dashing hopes for such a lower
bound.
A closer look at the protocol achieving the upper bound shows that
all but one of the players involved are collapsing, i.e., their
messages depend only on the composition of the layers ahead of
them. We consider protocols for the pointer jumping problem where
all players are collapsing. Our second result shows that a strong
$n - O(log n)$ lower bound does hold in this case. Our third
result is another upper bound showing that nontrivial protocols for
(a non-Boolean version of) pointer jumping are possible even when
all players are collapsing.
Our lower bound result uses a novel proof technique, different from
those of earlier lower bounds that had an information-theoretic
flavor. We hope this is useful in further study of the problem.
Cite as
Joshua Brody and Amit Chakrabarti. Sublinear Communication Protocols for Multi-Party Pointer Jumping and a Related Lower Bound. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 145-156, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{brody_et_al:LIPIcs.STACS.2008.1341,
author = {Brody, Joshua and Chakrabarti, Amit},
title = {{Sublinear Communication Protocols for Multi-Party Pointer Jumping and a Related Lower Bound}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {145--156},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1341},
URN = {urn:nbn:de:0030-drops-13415},
doi = {10.4230/LIPIcs.STACS.2008.1341},
annote = {Keywords: Communication complexity, pointer jumping, number on the forehead}
}
Document
Finding Irrefutable Certificates for S_2^p via Arthur and Merlin
Abstract
We show that $S_2^psubseteq P^{prAM}$, where $S_2^p$ is the
symmetric alternation class and $prAM$ refers to the promise
version of the Arthur-Merlin class $AM$. This is derived as a
consequence of our main result that presents an $FP^{prAM}$
algorithm for finding a small set of ``collectively irrefutable
certificates'' of a given $S_2$-type matrix. The main result also
yields some new consequences of the hypothesis that $NP$ has
polynomial size circuits. It is known that the above hypothesis
implies a collapse of the polynomial time hierarchy ($PH$) to
$S_2^psubseteq ZPP^{NP}$ (Cai 2007, K"obler and Watanabe 1998).
Under the same hypothesis, we show that $PH$ collapses to
$P^{prMA}$. We also describe an $FP^{prMA}$ algorithm for learning
polynomial size circuits for $SAT$, assuming such circuits exist.
For the same problem, the previously best known result was a
$ZPP^{NP}$ algorithm (Bshouty et al. 1996).
Cite as
Venkatesan T. Chakaravarthy and Sambuddha Roy. Finding Irrefutable Certificates for S_2^p via Arthur and Merlin. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 157-168, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{chakaravarthy_et_al:LIPIcs.STACS.2008.1342,
author = {Chakaravarthy, Venkatesan T. and Roy, Sambuddha},
title = {{Finding Irrefutable Certificates for S\underline2^p via Arthur and Merlin}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {157--168},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1342},
URN = {urn:nbn:de:0030-drops-13421},
doi = {10.4230/LIPIcs.STACS.2008.1342},
annote = {Keywords: Symmetric alternation, promise-AM, Karp--Lipton theorem, learning circuits}
}
Document
Quantifying Homology Classes
Abstract
We develop a method for measuring homology classes. This involves
three problems. First, we define the size of a homology class,
using ideas from relative homology. Second, we define an optimal
basis of a homology group to be the basis whose elements' size have
the minimal sum. We provide a greedy algorithm to compute the
optimal basis and measure classes in it. The algorithm runs in
$O(\beta^4 n^3 log^2 n)$ time, where $n$ is the size of the
simplicial complex and $\beta$ is the Betti number of the homology
group. Third, we discuss different ways of localizing homology
classes and prove some hardness results.
Cite as
Chao Chen and Daniel Freedman. Quantifying Homology Classes. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 169-180, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{chen_et_al:LIPIcs.STACS.2008.1343,
author = {Chen, Chao and Freedman, Daniel},
title = {{Quantifying Homology Classes}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {169--180},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1343},
URN = {urn:nbn:de:0030-drops-13434},
doi = {10.4230/LIPIcs.STACS.2008.1343},
annote = {Keywords: Computational Topology, Computational Geometry, Homology, Persistent Homology, Localization, Optimization}
}
Document
Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs
Abstract
Let $G$ be a directed planar graph of complexity~$n$, each arc
having a nonnegative length. Let $s$ and~$t$ be two distinct faces
of~$G$; let $s_1,ldots,s_k$ be vertices incident with~$s$; let
$t_1,ldots,t_k$ be vertices incident with~$t$. We give an
algorithm to compute $k$ pairwise vertex-disjoint paths connecting
the pairs $(s_i,t_i)$ in~$G$, with minimal total length, in
$O(knlog n)$ time.
Cite as
Éric Colin de Verdiére and Alexander Schrijver. Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 181-192, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{colindeverdiere_et_al:LIPIcs.STACS.2008.1347,
author = {Colin de Verdi\'{e}re, \'{E}ric and Schrijver, Alexander},
title = {{Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {181--192},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1347},
URN = {urn:nbn:de:0030-drops-13474},
doi = {10.4230/LIPIcs.STACS.2008.1347},
annote = {Keywords: Algorithm, planar graph, disjoint paths, shortest path}
}
Document
Geodesic Fréchet Distance Inside a Simple Polygon
Abstract
We unveil an alluring alternative to parametric search that applies
to both the non-geodesic and geodesic Fr{'\e}chet optimization
problems. This randomized approach is based on a variant of
red-blue intersections and is appealing due to its elegance and
practical efficiency when compared to parametric search.
We present the first algorithm for the geodesic Fr{'\e}chet distance
between two polygonal curves $A$ and $B$ inside a simple bounding
polygon $P$. The geodesic Fr{'\e}chet decision problem is solved
almost as fast as its non-geodesic sibling and requires $O(N^{2log
k)$ time and $O(k+N)$ space after $O(k)$ preprocessing, where $N$
is the larger of the complexities of $A$ and $B$ and $k$ is the
complexity of $P$. The geodesic Fr{'\e}chet optimization problem is
solved by a randomized approach in $O(k+N^{2log kNlog N)$
expected time and $O(k+N^{2)$ space. This runtime is only a
logarithmic factor larger than the standard non-geodesic Fr{'\e}chet
algorithm (Alt and Godau 1995). Results are also presented for the
geodesic Fr{'\e}chet distance in a polygonal domain with obstacles and
the geodesic Hausdorff distance for sets of points or sets of line
segments inside a simple polygon $P$.
Cite as
Carola Wenk and Atlas F. Cook. Geodesic Fréchet Distance Inside a Simple Polygon. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 193-204, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{wenk_et_al:LIPIcs.STACS.2008.1330,
author = {Wenk, Carola and Cook, Atlas F.},
title = {{Geodesic Fr\'{e}chet Distance Inside a Simple Polygon}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {193--204},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1330},
URN = {urn:nbn:de:0030-drops-13303},
doi = {10.4230/LIPIcs.STACS.2008.1330},
annote = {Keywords: Fr\'{e}chet Distance, Geodesic, Parametric Search, Simple Polygon}
}
Document
Improved Algorithms for the Range Next Value Problem and Applications
Abstract
The Range Next Value problem (Problem RNV) is a recent interesting
variant of the range search problems, where the query is for the
immediate next (or equal) value of a given number within a given
interval of an array. Problem RNV was introduced and studied very
recently by Crochemore et. al [Finding Patterns In Given
Intervals, MFCS 2007]. In this paper, we present improved
algorithms for Problem RNV. We also show how this problem can be
used to achieve optimal query time for a number of interesting
variants of the classic pattern matching problems.
Cite as
Costas S. Iliopoulos, Maxime Crochemore, Marcin Kubica, M. Sohel Rahman, and Tomasz Walen. Improved Algorithms for the Range Next Value Problem and Applications. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 205-216, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{iliopoulos_et_al:LIPIcs.STACS.2008.1359,
author = {Iliopoulos, Costas S. and Crochemore, Maxime and Kubica, Marcin and Rahman, M. Sohel and Walen, Tomasz},
title = {{Improved Algorithms for the Range Next Value Problem and Applications}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {205--216},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1359},
URN = {urn:nbn:de:0030-drops-13596},
doi = {10.4230/LIPIcs.STACS.2008.1359},
annote = {Keywords: Algorithms, Data structures}
}
Document
Connecting Polygonizations via Stretches and Twangs
Abstract
We show that the space of polygonizations of a fixed planar point
set $S$ of $n$ points is connected by $O(n^2)$ ``moves'' between
simple polygons. Each move is composed of a sequence of atomic
moves called ``stretches'' and ``twangs''. These atomic moves walk
between weakly simple ``polygonal wraps'' of $S$. These moves show
promise to serve as a basis for generating random polygons.
Cite as
Mirela Damian, Robin Flatland, Joseph O'Rourke, and Suneeta Ramaswani. Connecting Polygonizations via Stretches and Twangs. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 217-228, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{damian_et_al:LIPIcs.STACS.2008.1345,
author = {Damian, Mirela and Flatland, Robin and O'Rourke, Joseph and Ramaswani, Suneeta},
title = {{Connecting Polygonizations via Stretches and Twangs}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {217--228},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1345},
URN = {urn:nbn:de:0030-drops-13457},
doi = {10.4230/LIPIcs.STACS.2008.1345},
annote = {Keywords: Polygons, polygonization, random polygons, connected configuration space}
}
Document
Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs
Abstract
We present a deterministic way of assigning small (log bit) weights
to the edges of a bipartite planar graph so that the minimum weight
perfect matching becomes unique. The isolation lemma as described
in (Mulmuley et al. 1987) achieves the same for general graphs
using a randomized weighting scheme, whereas we can do it
deterministically when restricted to bipartite planar graphs. As a
consequence, we reduce both decision and construction versions of
the matching problem to testing whether a matrix is singular, under
the promise that its determinant is $0$ or $1$, thus obtaining a
highly parallel SPL algorithm for bipartite planar graphs. This
improves the earlier known bounds of non-uniform SPL by (Allender
et al. 1999) and $NC^2$ by (Miller and Naor 1995, Mahajan and
Varadarajan 2000). It also rekindles the hope of obtaining a
deterministic parallel algorithm for constructing a perfect
matching in non-bipartite planar graphs, which has been open for a
long time. Our techniques are elementary and simple.
Cite as
Samir Datta, Raghav Kulkarni, and Sambuddha Roy. Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 229-240, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{datta_et_al:LIPIcs.STACS.2008.1346,
author = {Datta, Samir and Kulkarni, Raghav and Roy, Sambuddha},
title = {{Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {229--240},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1346},
URN = {urn:nbn:de:0030-drops-13465},
doi = {10.4230/LIPIcs.STACS.2008.1346},
annote = {Keywords: }
}
Document
Tight Bounds for Blind Search on the Integers
Abstract
We analyze a simple random process in which a token is moved in the
interval $A={0,dots,n$: Fix a probability distribution $mu$
over ${1,dots,n$. Initially, the token is placed in a random
position in $A$. In round $t$, a random value $d$ is chosen
according to $mu$. If the token is in position $ageq d$, then it
is moved to position $a-d$. Otherwise it stays put. Let $T$ be
the number of rounds until the token reaches position 0. We show
tight bounds for the expectation of $T$ for the optimal
distribution $mu$. More precisely, we show that
$min_mu{E_mu(T)=Thetaleft((log n)^2
ight)$. For the
proof, a novel potential function argument is introduced. The
research is motivated by the problem of approximating the minimum
of a continuous function over $[0,1]$ with a ``blind'' optimization
strategy.
Cite as
Martin Dietzfelbinger, Jonathan E. Rowe, Ingo Wegener, and Philipp Woelfel. Tight Bounds for Blind Search on the Integers. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 241-252, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{dietzfelbinger_et_al:LIPIcs.STACS.2008.1348,
author = {Dietzfelbinger, Martin and Rowe, Jonathan E. and Wegener, Ingo and Woelfel, Philipp},
title = {{Tight Bounds for Blind Search on the Integers}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {241--252},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1348},
URN = {urn:nbn:de:0030-drops-13486},
doi = {10.4230/LIPIcs.STACS.2008.1348},
annote = {Keywords: }
}
Document
Discrete Jordan Curve Theorem: A proof formalized in Coq with hypermaps
Abstract
This paper presents a formalized proof of a discrete form of the
Jordan Curve Theorem. It is based on a hypermap model of planar
subdivisions, formal specifications and proofs assisted by the Coq
system. Fundamental properties are proven by structural or
noetherian induction: Genus Theorem, Euler's Formula, constructive
planarity criteria. A notion of ring of faces is inductively
defined and a Jordan Curve Theorem is stated and proven for any
planar hypermap.
Cite as
Jean-Francois Dufourd. Discrete Jordan Curve Theorem: A proof formalized in Coq with hypermaps. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 253-264, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{dufourd:LIPIcs.STACS.2008.1349,
author = {Dufourd, Jean-Francois},
title = {{Discrete Jordan Curve Theorem: A proof formalized in Coq with hypermaps}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {253--264},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1349},
URN = {urn:nbn:de:0030-drops-13493},
doi = {10.4230/LIPIcs.STACS.2008.1349},
annote = {Keywords: Formal specifications, Computational topology, Computer-aided proofs, Coq, Planar subdivisions, Hypermaps, Jordan Curve Theorem}
}
Document
Trimming of Graphs, with Application to Point Labeling
Abstract
For $t,g>0$, a vertex-weighted graph of total weight $W$ is
$(t,g)$-trimmable if it contains a vertex-induced subgraph of total
weight at least $(1-1/t)W$ and with no simple path of more than $g$
edges. A family of graphs is trimmable if for each constant $t>0$,
there is a constant $g=g(t)$ such that every vertex-weighted graph
in the family is $(t,g)$-trimmable. We show that every family of
graphs of bounded domino treewidth is trimmable. This implies that
every family of graphs of bounded degree is trimmable if the graphs
in the family have bounded treewidth or are planar. Based on this
result, we derive a polynomial-time approximation scheme for the
problem of labeling weighted points with nonoverlapping sliding
labels of unit height and given lengths so as to maximize the total
weight of the labeled points. This settles one of the last major
open questions in the theory of map labeling.
Cite as
Thomas Erlebach, Torben Hagerup, Klaus Jansen, Moritz Minzlaff, and Alexander Wolff. Trimming of Graphs, with Application to Point Labeling. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 265-276, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{erlebach_et_al:LIPIcs.STACS.2008.1350,
author = {Erlebach, Thomas and Hagerup, Torben and Jansen, Klaus and Minzlaff, Moritz and Wolff, Alexander},
title = {{Trimming of Graphs, with Application to Point Labeling}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {265--276},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1350},
URN = {urn:nbn:de:0030-drops-13509},
doi = {10.4230/LIPIcs.STACS.2008.1350},
annote = {Keywords: Trimming weighted graphs, domino treewidth, planar graphs, point-feature label placement, map labeling, polynomial-time approximation schemes}
}
Document
Computing Minimum Spanning Trees with Uncertainty
Abstract
We consider the minimum spanning tree problem in a setting where
information about the edge weights of the given graph is uncertain.
Initially, for each edge $e$ of the graph only a set $A_e$, called
an uncertainty area, that contains the actual edge weight
$w_e$ is known. The algorithm can `update' $e$ to obtain the edge
weight $w_e in A_e$. The task is to output the edge set of a
minimum spanning tree after a minimum number of updates. An
algorithm is $k$-update competitive if it makes at most $k$ times
as many updates as the optimum. We present a $2$-update
competitive algorithm if all areas $A_e$ are open or trivial, which
is the best possible among deterministic algorithms. The condition
on the areas $A_e$ is to exclude degenerate inputs for which no
constant update competitive algorithm can exist.
Next, we consider a setting where the vertices of the graph
correspond to points in Euclidean space and the weight of an edge
is equal to the distance of its endpoints. The location of each
point is initially given as an uncertainty area, and an update
reveals the exact location of the point. We give a general
relation between the edge uncertainty and the vertex uncertainty
versions of a problem and use it to derive a $4$-update competitive
algorithm for the minimum spanning tree problem in the vertex
uncertainty model. Again, we show that this is best possible among
deterministic algorithms.
Cite as
Michael Hoffmann, Thomas Erlebach, Danny Krizanc, Matús Mihal'ák, and Rajeev Raman. Computing Minimum Spanning Trees with Uncertainty. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 277-288, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{hoffmann_et_al:LIPIcs.STACS.2008.1358,
author = {Hoffmann, Michael and Erlebach, Thomas and Krizanc, Danny and Mihal'\'{a}k, Mat\'{u}s and Raman, Rajeev},
title = {{Computing Minimum Spanning Trees with Uncertainty}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {277--288},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1358},
URN = {urn:nbn:de:0030-drops-13581},
doi = {10.4230/LIPIcs.STACS.2008.1358},
annote = {Keywords: Algorithms and data structures; Current challenges: mobile and net computing}
}
Document
Convergence Thresholds of Newton's Method for Monotone Polynomial Equations
Abstract
Monotone systems of polynomial equations (MSPEs) are systems of
fixed-point equations $X_1 = f_1(X_1, ldots, X_n),$ $ldots, X_n =
f_n(X_1, ldots, X_n)$ where each $f_i$ is a polynomial with
positive real coefficients. The question of computing the least
non-negative solution of a given MSPE $vec X = vec f(vec X)$
arises naturally in the analysis of stochastic models such as
stochastic context-free grammars, probabilistic pushdown automata,
and back-button processes. Etessami and Yannakakis have recently
adapted Newton's iterative method to MSPEs. In a previous paper we
have proved the existence of a threshold $k_{vec f}$ for strongly
connected MSPEs, such that after $k_{vec f}$ iterations of
Newton's method each new iteration computes at least 1 new bit of
the solution. However, the proof was purely existential. In this
paper we give an upper bound for $k_{vec f}$ as a function of the
minimal component of the least fixed-point $muvec f$ of $vec
f(vec X)$. Using this result we show that $k_{vec f}$ is at most
single exponential resp. linear for strongly connected MSPEs
derived from probabilistic pushdown automata resp. from
back-button processes. Further, we prove the existence of a
threshold for arbitrary MSPEs after which each new iteration
computes at least $1/w2^h$ new bits of the solution, where $w$ and
$h$ are the width and height of the DAG of strongly connected
components.
Cite as
Javier Esparza, Stefan Kiefer, and Michael Luttenberger. Convergence Thresholds of Newton's Method for Monotone Polynomial Equations. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 289-300, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{esparza_et_al:LIPIcs.STACS.2008.1351,
author = {Esparza, Javier and Kiefer, Stefan and Luttenberger, Michael},
title = {{Convergence Thresholds of Newton's Method for Monotone Polynomial Equations}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {289--300},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1351},
URN = {urn:nbn:de:0030-drops-13516},
doi = {10.4230/LIPIcs.STACS.2008.1351},
annote = {Keywords: Newton's Method, Fixed-Point Equations, Formal Verification of Software, Probabilistic Pushdown Systems}
}
Document
Model Checking Games for the Quantitative µ-Calculus
Abstract
We investigate quantitative extensions of modal logic and the modal
$mu$-calculus, and study the question whether the tight connection
between logic and games can be lifted from the qualitative logics
to their quantitative counterparts. It turns out that, if the
quantitative $mu$-calculus is defined in an appropriate way
respecting the duality properties between the logical operators,
then its model checking problem can indeed be characterised by a
quantitative variant of parity games. However, these quantitative
games have quite different properties than their classical
counterparts, in particular they are, in general, not positionally
determined. The correspondence between the logic and the games
goes both ways: the value of a formula on a quantitative transition
system coincides with the value of the associated quantitative
game, and conversely, the values of quantitative parity games are
definable in the quantitative $mu$-calculus.
Cite as
Diana Fischer, Erich Grädel, and Lukasz Kaiser. Model Checking Games for the Quantitative µ-Calculus. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 301-312, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{fischer_et_al:LIPIcs.STACS.2008.1352,
author = {Fischer, Diana and Gr\"{a}del, Erich and Kaiser, Lukasz},
title = {{Model Checking Games for the Quantitative µ-Calculus}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {301--312},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1352},
URN = {urn:nbn:de:0030-drops-13525},
doi = {10.4230/LIPIcs.STACS.2008.1352},
annote = {Keywords: Games, logic, model checking, quantitative logics}
}
Document
Order-Invariant MSO is Stronger than Counting MSO in the Finite
Abstract
We compare the expressiveness of two extensions of monadic
second-order logic (MSO) over the class of finite structures. The
first, counting monadic second-order logic (CMSO), extends MSO with
first-order modulo-counting quantifiers, allowing the expression of
queries like ``the number of elements in the structure is even''.
The second extension allows the use of an additional binary
predicate, not contained in the signature of the queried structure,
that must be interpreted as an arbitrary linear order on its
universe, obtaining order-invariant MSO.
While it is straightforward that every CMSO formula can be
translated into an equivalent order-invariant MSO formula, the
converse had not yet been settled. Courcelle showed that for
restricted classes of structures both order-invariant MSO and CMSO
are equally expressive, but conjectured that, in general,
order-invariant MSO is stronger than CMSO.
We affirm this conjecture by presenting a class of structures that
is order-invariantly definable in MSO but not definable in CMSO.
Cite as
Tobias Ganzow and Sasha Rubin. Order-Invariant MSO is Stronger than Counting MSO in the Finite. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 313-324, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{ganzow_et_al:LIPIcs.STACS.2008.1353,
author = {Ganzow, Tobias and Rubin, Sasha},
title = {{Order-Invariant MSO is Stronger than Counting MSO in the Finite}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {313--324},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1353},
URN = {urn:nbn:de:0030-drops-13535},
doi = {10.4230/LIPIcs.STACS.2008.1353},
annote = {Keywords: MSO, Counting MSO, order-invariance, expressiveness, Ehrenfeucht-Fraiss\'{e} game}
}
Document
Succinctness of the Complement and Intersection of Regular Expressions
Abstract
We study the succinctness of the complement and intersection of
regular expressions. In particular, we show that when constructing
a regular expression defining the complement of a given regular
expression, a double exponential size increase cannot be avoided.
Similarly, when constructing a regular expression defining the
intersection of a fixed and an arbitrary number of regular
expressions, an exponential and double exponential size increase,
respectively, can in worst-case not be avoided. All mentioned
lower bounds improve the existing ones by one exponential and are
tight in the sense that the target expression can be constructed in
the corresponding time class, i.e., exponential or double
exponential time. As a by-product, we generalize a theorem by
Ehrenfeucht and Zeiger stating that there is a class of DFAs which
are exponentially more succinct than regular expressions, to a
fixed four-letter alphabet. When the given regular expressions are
one-unambiguous, as for instance required by the XML Schema
specification, the complement can be computed in polynomial time
whereas the bounds concerning intersection continue to hold. For
the subclass of single-occurrence regular expressions, we prove a
tight exponential lower bound for intersection.
Cite as
Wouter Gelade and Frank Neven. Succinctness of the Complement and Intersection of Regular Expressions. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 325-336, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{gelade_et_al:LIPIcs.STACS.2008.1354,
author = {Gelade, Wouter and Neven, Frank},
title = {{Succinctness of the Complement and Intersection of Regular Expressions}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {325--336},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1354},
URN = {urn:nbn:de:0030-drops-13541},
doi = {10.4230/LIPIcs.STACS.2008.1354},
annote = {Keywords: }
}
Document
Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages
Abstract
The purpose of this paper is to provide efficient algorithms that
decide membership for classes of several Boolean hierarchies for
which efficiency (or even decidability) were previously not known.
We develop new forbidden-chain characterizations for the single
levels of these hierarchies and obtain the following results:
- The classes of the Boolean hierarchy over level $Sigma_1$ of the
dot-depth hierarchy are decidable in $NL$ (previously only the
decidability was known). The same remains true if predicates mod
$d$ for fixed $d$ are allowed.
- If modular predicates for arbitrary $d$ are allowed, then the
classes of the Boolean hierarchy over level $Sigma_1$ are
decidable.
- For the restricted case of a two-letter alphabet, the classes of
the Boolean hierarchy over level $Sigma_2$ of the
Straubing-Th{'\e}rien hierarchy are decidable in $NL$. This is
the first decidability result for this hierarchy.
- The membership problems for all mentioned Boolean-hierarchy
classes are logspace many-one hard for $NL$.
- The membership problems for quasi-aperiodic languages and for
$d$-quasi-aperiodic languages are logspace many-one complete for
$PSPACE$.
Cite as
Christian Glasser, Heinz Schmitz, and Victor Selivanov. Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 337-348, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{glasser_et_al:LIPIcs.STACS.2008.1355,
author = {Glasser, Christian and Schmitz, Heinz and Selivanov, Victor},
title = {{Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {337--348},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1355},
URN = {urn:nbn:de:0030-drops-13554},
doi = {10.4230/LIPIcs.STACS.2008.1355},
annote = {Keywords: Automata and formal languages, computational complexity, dot-depth hierarchy, Boolean hierarchy, decidability, efficient algorithms}
}
Document
On the Complexity of Elementary Modal Logics
Abstract
Modal logics are widely used in computer science. The complexity
of modal satisfiability problems has been investigated since the
1970s, usually proving results on a case-by-case basis. We prove a
very general classification for a wide class of relevant logics:
Many important subclasses of modal logics can be obtained by
restricting the allowed models with first-order Horn formulas. We
show that the satisfiability problem for each of these logics is
either NP-complete or PSPACE-hard, and exhibit a simple
classification criterion. Further, we prove matching PSPACE upper
bounds for many of the PSPACE-hard logics.
Cite as
Edith Hemaspaandra and Henning Schnoor. On the Complexity of Elementary Modal Logics. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 349-360, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{hemaspaandra_et_al:LIPIcs.STACS.2008.1356,
author = {Hemaspaandra, Edith and Schnoor, Henning},
title = {{On the Complexity of Elementary Modal Logics}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {349--360},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1356},
URN = {urn:nbn:de:0030-drops-13561},
doi = {10.4230/LIPIcs.STACS.2008.1356},
annote = {Keywords: }
}
Document
Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible Supertrees
Abstract
Consider a set of labels $L$ and a set of trees ${mathcal T} = {
{mathcal T}^{(1), {mathcal T}^{(2), ldots, {mathcal T}^{(k) $
where each tree ${mathcal T}^{(i)$ is distinctly leaf-labeled by
some subset of $L$. One fundamental problem is to find the biggest
tree (denoted as supertree) to represent $mathcal T}$ which
minimizes the disagreements with the trees in ${mathcal T}$ under
certain criteria. This problem finds applications in
phylogenetics, database, and data mining. In this paper, we focus
on two particular supertree problems, namely, the maximum agreement
supertree problem (MASP) and the maximum compatible supertree
problem (MCSP). These two problems are known to be NP-hard for $k
geq 3$. This paper gives the first polynomial time algorithms for
both MASP and MCSP when both $k$ and the maximum degree $D$ of the
trees are constant.
Cite as
Viet Tung Hoang and Wing-Kin Sung. Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible Supertrees. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 361-372, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{hoang_et_al:LIPIcs.STACS.2008.1357,
author = {Hoang, Viet Tung and Sung, Wing-Kin},
title = {{Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible Supertrees}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {361--372},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1357},
URN = {urn:nbn:de:0030-drops-13579},
doi = {10.4230/LIPIcs.STACS.2008.1357},
annote = {Keywords: Maximum agreement supertree, maximum compatible supertree}
}
Document
Complexity of solutions of equations over sets of natural numbers
Abstract
Systems of equations over sets of natural numbers (or,
equivalently, language equations over a one-letter alphabet) of the
form $X_i=varphi_i(X_1, ldots, X_n)$ ($1 leqslant i leqslant
n$) are considered. Expressions $varphi_i$ may contain the
operations of union, intersection and pairwise sum $A plus B = {x
+ y mid x in A, y in B$. A system with an EXPTIME-complete
least solution is constructed, and it is established that least
solutions of all such systems are in EXPTIME. The general
membership problem for these equations is proved to be
EXPTIME-complete.
Cite as
Alexander Okhotin and Artur Jez. Complexity of solutions of equations over sets of natural numbers. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 373-384, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{okhotin_et_al:LIPIcs.STACS.2008.1319,
author = {Okhotin, Alexander and Jez, Artur},
title = {{Complexity of solutions of equations over sets of natural numbers}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {373--384},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1319},
URN = {urn:nbn:de:0030-drops-13194},
doi = {10.4230/LIPIcs.STACS.2008.1319},
annote = {Keywords: }
}
Document
Cardinality and counting quantifiers on omega-automatic structures
Abstract
We investigate structures that can be represented by
omega-automata, so called omega-automatic structures, and prove
that relations defined over such structures in first-order logic
expanded by the first-order quantifiers `there exist at most
$aleph_0$ many', 'there exist finitely many' and 'there exist $k$
modulo $m$ many' are omega-regular. The proof identifies certain
algebraic properties of omega-semigroups.
As a consequence an omega-regular equivalence relation of countable
index has an omega-regular set of representatives. This implies
Blumensath's conjecture that a countable structure with an
$omega$-automatic presentation can be represented using automata
on finite words. This also complements a very recent result of
Hj"orth, Khoussainov, Montalban and Nies showing that there is an
omega-automatic structure which has no injective presentation.
Cite as
Lukasz Kaiser, Sasha Rubin, and Vince Bárány. Cardinality and counting quantifiers on omega-automatic structures. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 385-396, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{kaiser_et_al:LIPIcs.STACS.2008.1360,
author = {Kaiser, Lukasz and Rubin, Sasha and B\'{a}r\'{a}ny, Vince},
title = {{Cardinality and counting quantifiers on omega-automatic structures}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {385--396},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1360},
URN = {urn:nbn:de:0030-drops-13602},
doi = {10.4230/LIPIcs.STACS.2008.1360},
annote = {Keywords: \$omega\$-automatic presentations, \$omega\$-semigroups, \$omega\$-automata}
}
Document
On the Induced Matching Problem
Abstract
We study extremal questions on induced matchings in several natural
graph classes. We argue that these questions should be asked for
twinless graphs, that is graphs not containing two vertices with
the same neighborhood. We show that planar twinless graphs always
contain an induced matching of size at least $n/40$ while there are
planar twinless graphs that do not contain an induced matching of
size $(n+10)/27$. We derive similar results for outerplanar graphs
and graphs of bounded genus. These extremal results can be applied
to the area of parameterized computation. For example, we show
that the induced matching problem on planar graphs has a kernel of
size at most $40k$ that is computable in linear time; this
significantly improves the results of Moser and Sikdar (2007). We
also show that we can decide in time $O(91^k + n)$ whether a planar
graph contains an induced matching of size at least $k$.
Cite as
Iyad A. Kanj, Michael J. Pelsmajer, Ge Xia, and Marcus Schaefer. On the Induced Matching Problem. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 397-408, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{kanj_et_al:LIPIcs.STACS.2008.1361,
author = {Kanj, Iyad A. and Pelsmajer, Michael J. and Xia, Ge and Schaefer, Marcus},
title = {{On the Induced Matching Problem}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {397--408},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1361},
URN = {urn:nbn:de:0030-drops-13618},
doi = {10.4230/LIPIcs.STACS.2008.1361},
annote = {Keywords: Induced matching, bounded genus graphs, parameterized algorithms, kernel}
}
Document
On Geometric Spanners of Euclidean and Unit Disk Graphs
Abstract
We consider the problem of constructing bounded-degree planar
geometric spanners of Euclidean and unit-disk graphs. It is well
known that the Delaunay subgraph is a planar geometric spanner with
stretch factor $C_{delapprox 2.42$; however, its degree may not be
bounded. Our first result is a very simple linear time algorithm
for constructing a subgraph of the Delaunay graph with stretch
factor $
ho =1+2pi(kcos{frac{pi{k)^{-1$ and degree bounded by
$k$, for any integer parameter $kgeq 14$. This result immediately
implies an algorithm for constructing a planar geometric spanner of
a Euclidean graph with stretch factor $
ho cdot C_{del$ and
degree bounded by $k$, for any integer parameter $kgeq 14$.
Moreover, the resulting spanner contains a Euclidean Minimum
Spanning Tree (EMST) as a subgraph. Our second contribution lies
in developing the structural results necessary to transfer our
analysis and algorithm from Euclidean graphs to unit disk graphs,
the usual model for wireless ad-hoc networks. We obtain a very
simple distributed, {em strictly-localized algorithm that, given a
unit disk graph embedded in the plane, constructs a geometric
spanner with the above stretch factor and degree bound, and also
containing an EMST as a subgraph. The obtained results
dramatically improve the previous results in all aspects, as shown
in the paper.
Cite as
Ljubomir Perkovic and Iyad A. Kanj. On Geometric Spanners of Euclidean and Unit Disk Graphs. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 409-420, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{perkovic_et_al:LIPIcs.STACS.2008.1320,
author = {Perkovic, Ljubomir and Kanj, Iyad A.},
title = {{On Geometric Spanners of Euclidean and Unit Disk Graphs}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {409--420},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1320},
URN = {urn:nbn:de:0030-drops-13200},
doi = {10.4230/LIPIcs.STACS.2008.1320},
annote = {Keywords: Geometric spanner, euclidean graph, unit disk graph, wireless ad-hoc networks}
}
Document
The Frobenius Problem in a Free Monoid
Abstract
The classical Frobenius problem over ${mathbb N}$ is to compute
the largest integer $g$ not representable as a non-negative integer
linear combination of non-negative integers $x_1, x_2, ldots,
x_k$, where $gcd(x_1, x_2, ldots, x_k) = 1$. In this paper we
consider novel generalizations of the Frobenius problem to the
noncommutative setting of a free monoid. Unlike the commutative
case, where the bound on $g$ is quadratic, we are able to show
exponential or subexponential behavior for several analogues of
$g$, with the precise bound depending on the particular measure
chosen.
Cite as
Jui-Yi Kao, Jeffrey Shallit, and Zhi Xu. The Frobenius Problem in a Free Monoid. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 421-432, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{kao_et_al:LIPIcs.STACS.2008.1362,
author = {Kao, Jui-Yi and Shallit, Jeffrey and Xu, Zhi},
title = {{The Frobenius Problem in a Free Monoid}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {421--432},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1362},
URN = {urn:nbn:de:0030-drops-13620},
doi = {10.4230/LIPIcs.STACS.2008.1362},
annote = {Keywords: Combinatorics on words, Frobenius problem, free monoid}
}
Document
Space Hierarchy Results for Randomized Models
Abstract
We prove space hierarchy and separation results for randomized and
other semantic models of computation with advice. Previous works
on hierarchy and separation theorems for such models focused on
time as the resource. We obtain tighter results with space as the
resource. Our main theorems are the following. Let $s(n)$ be any
space-constructible function that is $Omega(log n)$ and such that
$s(a n) = O(s(n))$ for all constants $a$, and let $s'(n)$ be any
function that is $omega(s(n))$.
- There exists a language computable by two-sided error randomized
machines using $s'(n)$ space and one bit of advice that is not
computable by two-sided error randomized machines using $s(n)$
space and $min(s(n),n)$ bits of advice.
- There exists a language computable by zero-sided error randomized
machines in space $s'(n)$ with one bit of advice that is not
computable by one-sided error randomized machines using $s(n)$
space and $min(s(n),n)$ bits of advice.
The condition that $s(a n)=O(s(n))$ is a technical condition
satisfied by typical space bounds that are at most linear. We also
obtain weaker results that apply to generic semantic models of
computation.
Cite as
Jeff Kinne and Dieter van Melkebeek. Space Hierarchy Results for Randomized Models. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 433-444, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{kinne_et_al:LIPIcs.STACS.2008.1363,
author = {Kinne, Jeff and van Melkebeek, Dieter},
title = {{Space Hierarchy Results for Randomized Models}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {433--444},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1363},
URN = {urn:nbn:de:0030-drops-13636},
doi = {10.4230/LIPIcs.STACS.2008.1363},
annote = {Keywords: Computations with Advice, Space Hierarchy, Randomized Machine, Promise Classes, Semantic Models}
}
Document
Ehrenfeucht-Fraissé Goes Automatic for Real Addition
Abstract
Various logical theories can be decided by automata-theoretic
methods. Notable examples are Presburger arithmetic FO$(Z,+,<)$
and the linear arithmetic over the reals FO$(R,+,<)$, for which
effective decision procedures can be built using automata. Despite
the practical use of automata to decide logical theories, many
research questions are still only partly answered in this area.
One of these questions is the complexity of such decision
procedures and the related question about the minimal size of the
automata of the languages that can be described by formulas in the
respective logic. In this paper, we establish a double exponential
upper bound on the automata size for FO$(R,+,<)$ and an exponential
upper bound for the discrete order over the integers FO$(Z,<)$.
The proofs of these upper bounds are based on
Ehrenfeucht-Fraiss{'\e} games. The application of this
mathematical tool has a similar flavor as in computational
complexity theory, where it can often be used to establish tight
upper bounds of the decision problem for logical theories.
Cite as
Felix Klaedtke. Ehrenfeucht-Fraissé Goes Automatic for Real Addition. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 445-456, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{klaedtke:LIPIcs.STACS.2008.1364,
author = {Klaedtke, Felix},
title = {{Ehrenfeucht-Fraiss\'{e} Goes Automatic for Real Addition}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {445--456},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1364},
URN = {urn:nbn:de:0030-drops-13649},
doi = {10.4230/LIPIcs.STACS.2008.1364},
annote = {Keywords: Automata theory, automata-based decision procedures for logical theories, upper bounds, minimal sizes of automata, linear arithmetic over the reals, f}
}
Document
New Combinatorial Complete One-Way Functions
Abstract
In 2003, Leonid A. Levin presented the idea of a combinatorial
complete one-way function and a sketch of the proof that Tiling
represents such a function. In this paper, we present two new
one-way functions based on semi-Thue string rewriting systems and a
version of the Post Correspondence Problem and prove their
completeness. Besides, we present an alternative proof of Levin's
result. We also discuss the properties a combinatorial problem
should have in order to hold a complete one-way function.
Cite as
Arist Kojevnikov and Sergey I. Nikolenko. New Combinatorial Complete One-Way Functions. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 457-466, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{kojevnikov_et_al:LIPIcs.STACS.2008.1365,
author = {Kojevnikov, Arist and Nikolenko, Sergey I.},
title = {{New Combinatorial Complete One-Way Functions}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {457--466},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1365},
URN = {urn:nbn:de:0030-drops-13652},
doi = {10.4230/LIPIcs.STACS.2008.1365},
annote = {Keywords: }
}
Document
Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic
Abstract
We investigate the relation between the theory of the iterations in
the sense of Shelah-Stupp and of Muchnik, resp., and the theory of
the base structure for several logics. These logics are obtained
from the restriction of set quantification in monadic second order
logic to certain subsets like, e.g., finite sets, chains, and
finite unions of chains. We show that these theories of the
Shelah-Stupp iteration can be reduced to corresponding theories of
the base structure. This fails for Muchnik's iteration.
Cite as
Dietrich Kuske. Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 467-478, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{kuske:LIPIcs.STACS.2008.1366,
author = {Kuske, Dietrich},
title = {{Compatibility of Shelah and Stupp's and Muchnik's iteration with fragments of monadic second order logic}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {467--478},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1366},
URN = {urn:nbn:de:0030-drops-13668},
doi = {10.4230/LIPIcs.STACS.2008.1366},
annote = {Keywords: Logic in computer science, Rabin's tree theorem}
}
Document
Geometric Set Cover and Hitting Sets for Polytopes in R³
Abstract
Suppose we are given a finite set of points $P$ in $R^3$ and a
collection of polytopes $mathcal{T}$ that are all translates of
the same polytope $T$. We consider two problems in this paper.
The first is the set cover problem where we want to select a
minimal number of polytopes from the collection $mathcal{T}$ such
that their union covers all input points $P$. The second problem
that we consider is finding a hitting set for the set of polytopes
$mathcal{T}$, that is, we want to select a minimal number of
points from the input points $P$ such that every given polytope is
hit by at least one point.
We give the first constant-factor approximation algorithms for both
problems. We achieve this by providing an epsilon-net for
translates of a polytope in $R^3$ of size
$\bigO(frac{1{epsilon)$.
Cite as
Sören Lauen. Geometric Set Cover and Hitting Sets for Polytopes in R³. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 479-490, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{lauen:LIPIcs.STACS.2008.1367,
author = {Lauen, S\"{o}ren},
title = {{Geometric Set Cover and Hitting Sets for Polytopes in R³}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {479--490},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1367},
URN = {urn:nbn:de:0030-drops-13675},
doi = {10.4230/LIPIcs.STACS.2008.1367},
annote = {Keywords: Computational Geometry, Epsilon-Nets, Set Cover, Hitting Sets}
}
Document
Extended Abstract
A Theory for Valiant's Matchcircuits (Extended Abstract)
Abstract
The computational function of a matchgate is represented by its
character matrix. In this article, we show that all nonsingular
character matrices are closed under matrix inverse operation, so
that for every $k$, the nonsingular character matrices of $k$-bit
matchgates form a group, extending the recent work of Cai and
Choudhary (2006) of the same result for the case of $k=2$, and that
the single and the two-bit matchgates are universal for
matchcircuits, answering a question of Valiant (2002).
Cite as
Angsheng Li and Mingji Xia. A Theory for Valiant's Matchcircuits (Extended Abstract). In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 491-502, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{li_et_al:LIPIcs.STACS.2008.1368,
author = {Li, Angsheng and Xia, Mingji},
title = {{A Theory for Valiant's Matchcircuits}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {491--502},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1368},
URN = {urn:nbn:de:0030-drops-13686},
doi = {10.4230/LIPIcs.STACS.2008.1368},
annote = {Keywords: Pfaffian, Matchgate, Matchcircuit}
}
Document
Rent, Lease or Buy: Randomized Algorithms for Multislope Ski Rental
Abstract
In the Multislope Ski Rental problem, the user needs a certain
resource for some unknown period of time. To use the resource, the
user must subscribe to one of several options, each of which
consists of a one-time setup cost (``buying price''), and cost
proportional to the duration of the usage (``rental rate''). The
larger the price, the smaller the rent. The actual usage time is
determined by an adversary, and the goal of an algorithm is to
minimize the cost by choosing the best option at any point in time.
Multislope Ski Rental is a natural generalization of the classical
Ski Rental problem (where the only options are pure rent and pure
buy), which is one of the fundamental problems of online
computation. The Multislope Ski Rental problem is an abstraction
of many problems where online decisions cannot be modeled by just
two options, e.g., power management in systems which can be shut
down in parts. In this paper we study randomized algorithms for
Multislope Ski Rental. Our results include the best possible
online randomized strategy for any additive instance, where the
cost of switching from one option to another is the difference in
their buying prices; and an algorithm that produces an
$e$-competitive randomized strategy for any (non-additive)
instance.
Cite as
Zvi Lotker, Boaz Patt-Shamir, and Dror Rawitz. Rent, Lease or Buy: Randomized Algorithms for Multislope Ski Rental. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 503-514, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{lotker_et_al:LIPIcs.STACS.2008.1331,
author = {Lotker, Zvi and Patt-Shamir, Boaz and Rawitz, Dror},
title = {{Rent, Lease or Buy: Randomized Algorithms for Multislope Ski Rental}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {503--514},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1331},
URN = {urn:nbn:de:0030-drops-13313},
doi = {10.4230/LIPIcs.STACS.2008.1331},
annote = {Keywords: Competitive analysis, ski rental, randomized algorithms}
}
Document
Lower bounds for adaptive linearity tests
Abstract
Linearity tests are randomized algorithms which have oracle access
to the truth table of some function f, and are supposed to
distinguish between linear functions and functions which are far
from linear. Linearity tests were first introduced by (Blum, Luby
and Rubenfeld, 1993), and were later used in the PCP theorem,
among other applications. The quality of a linearity test is
described by its correctness c - the probability it accepts linear
functions, its soundness s - the probability it accepts functions
far from linear, and its query complexity q - the number of queries
it makes.
Linearity tests were studied in order to decrease the soundness of
linearity tests, while keeping the query complexity small (for one
reason, to improve PCP constructions). Samorodnitsky and Trevisan
(Samorodnitsky and Trevisan 2000) constructed the Complete Graph
Test, and prove that no Hyper Graph Test can perform better than
the Complete Graph Test. Later in (Samorodnitsky and Trevisan
2006) they prove, among other results, that no non-adaptive
linearity test can perform better than the Complete Graph Test.
Their proof uses the algebraic machinery of the Gowers Norm. A
result by (Ben-Sasson, Harsha and Raskhodnikova 2005) allows to
generalize this lower bound also to adaptive linearity tests.
We also prove the same optimal lower bound for adaptive linearity
test, but our proof technique is arguably simpler and more direct
than the one used in (Samorodnitsky and Trevisan 2006). We also
study, like (Samorodnitsky and Trevisan 2006), the behavior of
linearity tests on quadratic functions. However, instead of
analyzing the Gowers Norm of certain functions, we provide a more
direct combinatorial proof, studying the behavior of linearity
tests on random quadratic functions. This proof technique also
lets us prove directly the lower bound also for adaptive linearity
tests.
Cite as
Shachar Lovett. Lower bounds for adaptive linearity tests. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 515-526, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{lovett:LIPIcs.STACS.2008.1313,
author = {Lovett, Shachar},
title = {{Lower bounds for adaptive linearity tests}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {515--526},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1313},
URN = {urn:nbn:de:0030-drops-13132},
doi = {10.4230/LIPIcs.STACS.2008.1313},
annote = {Keywords: Property testing, Linearity testing, Adaptive tests, Lower Property testing, Linearity testing, Adaptive tests, Lower}
}
Document
Extended Abstract
Lagrangian Relaxation and Partial Cover (Extended Abstract)
Abstract
Lagrangian relaxation has been used extensively in the design of
approximation algorithms. This paper studies its strengths and
limitations when applied to Partial Cover.
We show that for Partial Cover in general no algorithm that uses
Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP)
$alpha$-approximation as a black box can yield an approximation
factor better than~$frac{4}{3} alpha$. This matches the upper bound
given by K"onemann et al. (ESA 2006, pages
468--479).
Faced with this limitation we study a specific, yet broad class of
covering problems: Partial Totally Balanced Cover. By carefully
analyzing the inner workings of the LMP algorithm we are able to
give an almost tight characterization of the integrality gap of the
standard linear relaxation of the problem. As a consequence we
obtain improved approximations for the Partial version of Multicut
and Path Hitting on Trees, Rectangle Stabbing, and Set Cover with
$
ho$-Blocks.
Cite as
Julián Mestre. Lagrangian Relaxation and Partial Cover (Extended Abstract). In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 539-550, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{mestre:LIPIcs.STACS.2008.1315,
author = {Mestre, Juli\'{a}n},
title = {{Lagrangian Relaxation and Partial Cover}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {539--550},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1315},
URN = {urn:nbn:de:0030-drops-13156},
doi = {10.4230/LIPIcs.STACS.2008.1315},
annote = {Keywords: Lagrangian Relaxation, Partial Cover, Primal-Dual Algorithms}
}
Document
An Improved Randomized Truthful Mechanism for Scheduling Unrelated Machines
Abstract
We study the scheduling problem on unrelated machines in the
mechanism design setting. This problem was proposed and studied in
the seminal paper (Nisan and Ronen 1999), where they gave a
$1.75$-approximation randomized truthful mechanism for the case of
two machines. We improve this result by a $1.6737$-approximation
randomized truthful mechanism. We also generalize our result to a
$0.8368m$-approximation mechanism for task scheduling with $m$
machines, which improve the previous best upper bound of
$0.875m( Mu'alem and Schapira 2007)
Cite as
Pinyan Lu and Changyuan Yu. An Improved Randomized Truthful Mechanism for Scheduling Unrelated Machines. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 527-538, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{lu_et_al:LIPIcs.STACS.2008.1314,
author = {Lu, Pinyan and Yu, Changyuan},
title = {{An Improved Randomized Truthful Mechanism for Scheduling Unrelated Machines}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {527--538},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1314},
URN = {urn:nbn:de:0030-drops-13146},
doi = {10.4230/LIPIcs.STACS.2008.1314},
annote = {Keywords: Truthful mechanism, scheduling}
}
Document
On Dynamic Breadth-First Search in External-Memory
Abstract
We provide the first non-trivial result on dynamic breadth-first
search (BFS) in external-memory: For general sparse undirected
graphs of initially $n$ nodes and $O(n)$ edges and monotone update
sequences of either $Theta(n)$ edge insertions or $Theta(n)$ edge
deletions, we prove an amortized high-probability bound of
$O(n/B^{2/3}+sort(n)cdot log B)$ I/Os per update. In contrast,
the currently best approach for static BFS on sparse undirected
graphs requires $Omega(n/B^{1/2}+sort(n))$ I/Os.
Cite as
Ulrich Meyer. On Dynamic Breadth-First Search in External-Memory. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 551-560, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{meyer:LIPIcs.STACS.2008.1316,
author = {Meyer, Ulrich},
title = {{On Dynamic Breadth-First Search in External-Memory}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {551--560},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1316},
URN = {urn:nbn:de:0030-drops-13167},
doi = {10.4230/LIPIcs.STACS.2008.1316},
annote = {Keywords: External Memory, Dynamic Graph Algorithms, BFS, Randomization}
}
Document
Analytic aspects of the shuffle product
Abstract
There exist very lucid explanations of the combinatorial origins of
rational and algebraic functions, in particular with respect to
regular and context free languages. In the search to understand
how to extend these natural correspondences, we find that the
shuffle product models many key aspects of D-finite generating
functions, a class which contains algebraic. We consider several
different takes on the shuffle product, shuffle closure, and
shuffle grammars, and give explicit generating function
consequences. In the process, we define a grammar class that
models D-finite generating functions.
Cite as
Marni Mishna and Mike Zabrocki. Analytic aspects of the shuffle product. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 561-572, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{mishna_et_al:LIPIcs.STACS.2008.1317,
author = {Mishna, Marni and Zabrocki, Mike},
title = {{Analytic aspects of the shuffle product}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {561--572},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1317},
URN = {urn:nbn:de:0030-drops-13178},
doi = {10.4230/LIPIcs.STACS.2008.1317},
annote = {Keywords: Generating functions, formal languages, shuffle product}
}
Document
Weak index versus Borel rank
Abstract
We investigate weak recognizability of deterministic languages of
infinite trees. We prove that for deterministic languages the
Borel hierarchy and the weak index hierarchy coincide.
Furthermore, we propose a procedure computing for a deterministic
automaton an equivalent minimal index weak automaton with a
quadratic number of states. The algorithm works within the time of
solving the emptiness problem.
Cite as
Filip Murlak. Weak index versus Borel rank. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 573-584, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{murlak:LIPIcs.STACS.2008.1318,
author = {Murlak, Filip},
title = {{Weak index versus Borel rank}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {573--584},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1318},
URN = {urn:nbn:de:0030-drops-13182},
doi = {10.4230/LIPIcs.STACS.2008.1318},
annote = {Keywords: Weak index, Borel rank, deterministic tree automata}
}
Document
A Mahler's theorem for functions from words to integers
Abstract
In this paper, we prove an extension of Mahler's theorem, a
celebrated result of $p$-adic analysis. Mahler's original result
states that a function from $N$ to $Z$ is uniformly continuous for
the $p$-adic metric $d_p$ if and only if it can be uniformly
approximated by polynomial functions. We prove the same result for
functions from $A^*$ to $Z$, where $d_p$ is now the profinite
metric defined by $p$-groups (pro-$p$ metric).
Cite as
Jean-Eric Pin and Pedro V. Silva. A Mahler's theorem for functions from words to integers. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 585-596, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{pin_et_al:LIPIcs.STACS.2008.1321,
author = {Pin, Jean-Eric and Silva, Pedro V.},
title = {{A Mahler's theorem for functions from words to integers}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {585--596},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1321},
URN = {urn:nbn:de:0030-drops-13212},
doi = {10.4230/LIPIcs.STACS.2008.1321},
annote = {Keywords: \$p\$-adic topology, binomial coefficients, Mahler's theorem, \$p\$-group languages}
}
Document
Distinguishing Short Quantum Computations
Abstract
Distinguishing logarithmic depth quantum circuits on mixed states
is shown to be complete for $QIP$, the class of problems having
quantum interactive proof systems. Circuits in this model can
represent arbitrary quantum processes, and thus this result has
implications for the verification of implementations of quantum
algorithms. The distinguishability problem is also complete for
$QIP$ on constant depth circuits containing the unbounded fan-out
gate. These results are shown by reducing a $QIP$-complete problem
to a logarithmic depth version of itself using a parallelization
technique.
Cite as
Bill Rosgen. Distinguishing Short Quantum Computations. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 597-608, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{rosgen:LIPIcs.STACS.2008.1322,
author = {Rosgen, Bill},
title = {{Distinguishing Short Quantum Computations}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {597--608},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1322},
URN = {urn:nbn:de:0030-drops-13222},
doi = {10.4230/LIPIcs.STACS.2008.1322},
annote = {Keywords: Quantum information, computational complexity, quantum circuits, quantum interactive proof systems}
}
Document
Factoring Polynomials over Finite Fields using Balance Test
Abstract
We study the problem of factoring univariate polynomials over
finite fields. Under the assumption of the Extended Riemann
Hypothesis (ERH), (Gao, 2001) designed a polynomial time algorithm
that fails to factor only if the input polynomial satisfies a
strong symmetry property, namely square balance. In this paper, we
propose an extension of Gao's algorithm that fails only under an
even stronger symmetry property. We also show that our property
can be used to improve the time complexity of best deterministic
algorithms on most input polynomials. The property also yields a
new randomized polynomial time algorithm.
Cite as
Chandan Saha. Factoring Polynomials over Finite Fields using Balance Test. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 609-620, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{saha:LIPIcs.STACS.2008.1323,
author = {Saha, Chandan},
title = {{Factoring Polynomials over Finite Fields using Balance Test}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {609--620},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1323},
URN = {urn:nbn:de:0030-drops-13233},
doi = {10.4230/LIPIcs.STACS.2008.1323},
annote = {Keywords: Algebraic Algorithms, polynomial factorization, finite fields}
}
Document
On the decomposition of k-valued rational relations
Abstract
We give a new, and hopefully more easily understandable, structural
proof of the decomposition of a $k$-valued transducer into $k$
unambiguous functional ones, a result established by A. Weber in
1996. Our construction is based on a lexicographic ordering of
computations of automata and on two coverings that can be build by
means of this ordering. The complexity of the construction,
measured as the number of states of the transducers involved in the
decomposition, improves the original one by one exponential.
Moreover, this method allows further generalisation that solves the
problem of decomposition of rational relations with bounded
length-degree, which was left open in Weber's paper.
Cite as
Jacques Sakarovitch and Rodrigo de Souza. On the decomposition of k-valued rational relations. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 621-632, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{sakarovitch_et_al:LIPIcs.STACS.2008.1324,
author = {Sakarovitch, Jacques and de Souza, Rodrigo},
title = {{On the decomposition of k-valued rational relations}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {621--632},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1324},
URN = {urn:nbn:de:0030-drops-13245},
doi = {10.4230/LIPIcs.STACS.2008.1324},
annote = {Keywords: Rational relation, \$k\$-valued transducer, unambiguous transducer, covering of automata}
}
Document
The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace
Abstract
The isomorphism problem for planar graphs is known to be
efficiently solvable. For planar 3-connected graphs, the
isomorphism problem can be solved by efficient parallel algorithms,
it is in the class $AC^1$.
In this paper we improve the upper bound for planar 3-connected
graphs to unambiguous logspace, in fact to $UL cap coUL$. As a
consequence of our method we get that the isomorphism problem for
oriented graphs is in $NL$. We also show that the problems are
hard for $L$.
Cite as
Thomas Thierauf and Fabian Wagner. The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 633-644, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{thierauf_et_al:LIPIcs.STACS.2008.1327,
author = {Thierauf, Thomas and Wagner, Fabian},
title = {{The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {633--644},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1327},
URN = {urn:nbn:de:0030-drops-13273},
doi = {10.4230/LIPIcs.STACS.2008.1327},
annote = {Keywords: }
}
Document
Efficient Minimization of DFAs with Partial Transition
Abstract
Let PT-DFA mean a deterministic finite automaton whose transition
relation is a partial function. We present an algorithm for
minimizing a PT-DFA in $O(m lg n)$ time and $O(m+n+alpha)$
memory, where $n$ is the number of states, $m$ is the number of
defined transitions, and $alpha$ is the size of the alphabet.
Time consumption does not depend on $alpha$, because the $alpha$
term arises from an array that is accessed at random and never
initialized. It is not needed, if transitions are in a suitable
order in the input. The algorithm uses two instances of an
array-based data structure for maintaining a refinable partition.
Its operations are all amortized constant time. One instance
represents the classical blocks and the other a partition of
transitions. Our measurements demonstrate the speed advantage of
our algorithm on PT-DFAs over an $O(alpha n lg n)$ time,
$O(alpha n)$ memory algorithm.
Cite as
Antti Valmari and Petri Lehtinen. Efficient Minimization of DFAs with Partial Transition. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 645-656, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{valmari_et_al:LIPIcs.STACS.2008.1328,
author = {Valmari, Antti and Lehtinen, Petri},
title = {{Efficient Minimization of DFAs with Partial Transition}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {645--656},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1328},
URN = {urn:nbn:de:0030-drops-13286},
doi = {10.4230/LIPIcs.STACS.2008.1328},
annote = {Keywords: Deterministic finite automaton, sparse adjacency matrix, partition refinement}
}
Document
Design by Measure and Conquer, A Faster Exact Algorithm for Dominating Set
Abstract
The measure and conquer approach has proven to be a powerful tool
to analyse exact algorithms for combinatorial problems, like
Dominating Set and Independent Set. In this paper, we propose to
use measure and conquer also as a tool in the design of algorithms.
In an iterative process, we can obtain a series of branch and
reduce algorithms. A mathematical analysis of an algorithm in the
series with measure and conquer results in a quasiconvex
programming problem. The solution by computer to this problem not
only gives a bound on the running time, but also can give a new
reduction rule, thus giving a new, possibly faster algorithm. This
makes design by measure and conquer a form of computer aided
algorithm design.
When we apply the methodology to a Set Cover modelling of the
Dominating Set problem, we obtain the currently fastest known exact
algorithms for Dominating Set: an algorithm that uses $O(1.5134^n)$
time and polynomial space, and an algorithm that uses $O(1.5063^n)$
time.
Cite as
Johan M. M. van Rooij and Hans L. Bodlaender. Design by Measure and Conquer, A Faster Exact Algorithm for Dominating Set. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 657-668, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{vanrooij_et_al:LIPIcs.STACS.2008.1329,
author = {van Rooij, Johan M. M. and Bodlaender, Hans L.},
title = {{Design by Measure and Conquer, A Faster Exact Algorithm for Dominating Set}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {657--668},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1329},
URN = {urn:nbn:de:0030-drops-13297},
doi = {10.4230/LIPIcs.STACS.2008.1329},
annote = {Keywords: Exact algorithms, exponential time algorithms, branch and reduce, measure and conquer, dominating set, computer aided algorithm design}
}
Document
Weighted Matching in the Semi-Streaming Model
Abstract
We reduce the best known approximation ratio for finding a weighted
matching of a graph using a one-pass semi-streaming algorithm from
5.828 to 5.585. The semi-streaming model forbids random access to
the input and restricts the memory to
$mathcal{O(ncdotmbox{polylog,n)$ bits. It was introduced by
Muthukrishnan in 2003 and is appropriate when dealing with massive
graphs.
Cite as
Mariano Zelke. Weighted Matching in the Semi-Streaming Model. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 669-680, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
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@InProceedings{zelke:LIPIcs.STACS.2008.1312,
author = {Zelke, Mariano},
title = {{Weighted Matching in the Semi-Streaming Model}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {669--680},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Albers, Susanne and Weil, Pascal},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1312},
URN = {urn:nbn:de:0030-drops-13128},
doi = {10.4230/LIPIcs.STACS.2008.1312},
annote = {Keywords: Semi-streaming algorithm, matching, approximation algorithm, graph algorithm}
}