136 Search Results for "Monmege, Benjamin"

Volume

LIPIcs, Volume 219

39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

STACS 2022, March 15-18, 2022, Marseille, France (Virtual Conference)

Editors: Petra Berenbrink and Benjamin Monmege

Volume

LIPIcs, Volume 187

38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

STACS 2021, March 16-19, 2021, Saarbrücken, Germany (Virtual Conference)

Editors: Markus Bläser and Benjamin Monmege

Document
DOI: 10.4230/LIPIcs.CONCUR.2022.15
Decidability of One-Clock Weighted Timed Games with Arbitrary Weights

Authors: Benjamin Monmege, Julie Parreaux, and Pierre-Alain Reynier

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
Weighted Timed Games (WTG for short) are the most widely used model to describe controller synthesis problems involving real-time issues. Unfortunately, they are notoriously difficult, and undecidable in general. As a consequence, one-clock WTG has attracted a lot of attention, especially because they are known to be decidable when only non-negative weights are allowed. However, when arbitrary weights are considered, despite several recent works, their decidability status was still unknown. In this paper, we solve this problem positively and show that the value function can be computed in exponential time (if weights are encoded in unary).
Cite as

Benjamin Monmege, Julie Parreaux, and Pierre-Alain Reynier. Decidability of One-Clock Weighted Timed Games with Arbitrary Weights. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{monmege_et_al:LIPIcs.CONCUR.2022.15,
  author =	{Monmege, Benjamin and Parreaux, Julie and Reynier, Pierre-Alain},
  title =	{{Decidability of One-Clock Weighted Timed Games with Arbitrary Weights}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.15},
  URN =		{urn:nbn:de:0030-drops-170786},
  doi =		{10.4230/LIPIcs.CONCUR.2022.15},
  annote =	{Keywords: Weighted timed games, Algorithmic game theory, Timed automata}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.STACS.2022
LIPIcs, Volume 219, STACS 2022, Complete Volume

Authors: Petra Berenbrink and Benjamin Monmege

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
LIPIcs, Volume 219, STACS 2022, Complete Volume
Cite as

39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 1-1044, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{berenbrink_et_al:LIPIcs.STACS.2022,
  title =	{{LIPIcs, Volume 219, STACS 2022, Complete Volume}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{1--1044},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022},
  URN =		{urn:nbn:de:0030-drops-158098},
  doi =		{10.4230/LIPIcs.STACS.2022},
  annote =	{Keywords: LIPIcs, Volume 219, STACS 2022, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.STACS.2022.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Petra Berenbrink and Benjamin Monmege

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{berenbrink_et_al:LIPIcs.STACS.2022.0,
  author =	{Berenbrink, Petra and Monmege, Benjamin},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.0},
  URN =		{urn:nbn:de:0030-drops-158101},
  doi =		{10.4230/LIPIcs.STACS.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2022.1
Local Limit of Random Discrete Surface with (Or Without!) a Statistical Physics Model (Invited Talk)

Authors: Marie Albenque

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
A planar map is an embedding of a planar graph in the sphere, considered up to deformations. A triangulation is a planar map, where all the faces are triangles. In 2003, in order to define a model of generic planar geometry, Angel and Schramm studied the limit of random triangulations on the sphere, [Angel and Schramm, 2003]. They proved that this model of random maps converges for the Benjamini-Schramm topology (see [Benjamini and Schramm, 2001]), or local topology, towards the now famous Uniform Infinite Planar Triangulation (or UIPT), a probability distribution on infinite triangulations, see Figure 1. Soon after, Angel [Angel, 2003] studied some properties of the UIPT. He established that the volume of the balls the UIPT of radius R scales as R⁴. Similar results (but with quite different proofs) were then obtained for quadrangulations by Chassaing and Durhuus and Krikun. The results cited above deal with models of maps that fall in the same "universality class", identified in the physics literature as the class of "pure 2D quantum gravity": the generating series all admit the same critical exponent and the volume of the balls of the local limits of several of those models of random maps are known to grow as R⁴. To capture this universal behaviour, a good framework is to consider scaling limits of random maps in the Gromov Hausdorff topology. Indeed, for a wide variety of models the scaling limit exists and is the so-called Brownian map [Le Gall, 2013; Miermont, 2013], see Figure 2. To escape this pure gravity behaviour, physicists have long ago understood that one should "couple gravity with matter", that is, consider models of random maps endowed with a statistical physics model. I will present in particular the case of triangulations decorated by an Ising model. It consists in colouring in black and white the vertices of a triangulation, and consider probability distribution which are now biased by their number of monochromatic edges. In a recent work, in collaboration with Laurent Ménard and Gilles Schaeffer [Albenque et al., 2020], we proved that the local limit of this model also exists. In this talk, I will present these results and explain the main ideas underlying their proof, which rely in part on some enumerative formulas obtained by Tutte in the 60s [Tutte, 1962], or their generalization to coloured triangulations by Bernardi and Bousquet-Mélou [Bernardi and Bousquet-Mélou, 2011].
Cite as

Marie Albenque. Local Limit of Random Discrete Surface with (Or Without!) a Statistical Physics Model (Invited Talk). In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{albenque:LIPIcs.STACS.2022.1,
  author =	{Albenque, Marie},
  title =	{{Local Limit of Random Discrete Surface with (Or Without!) a Statistical Physics Model}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{1:1--1:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.1},
  URN =		{urn:nbn:de:0030-drops-158118},
  doi =		{10.4230/LIPIcs.STACS.2022.1},
  annote =	{Keywords: Random graphs, triangulations, Benjamini-Schramm convergence, Ising model}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2022.2
Generalization Guarantees for Data-Driven Mechanism Design (Invited Talk)

Authors: Maria-Florina Balcan

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Many mechanisms including pricing mechanisms and auctions typically come with a variety of tunable parameters which impact significantly their desired performance guarantees. Data-driven mechanism design is a powerful approach for designing mechanisms, where these parameters are tuned via machine learning based on data. In this talk I will discuss how techniques from machine learning theory can be adapted and extended to analyze generalization guarantees of data-driven mechanism design.
Cite as

Maria-Florina Balcan. Generalization Guarantees for Data-Driven Mechanism Design (Invited Talk). In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{balcan:LIPIcs.STACS.2022.2,
  author =	{Balcan, Maria-Florina},
  title =	{{Generalization Guarantees for Data-Driven Mechanism Design}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.2},
  URN =		{urn:nbn:de:0030-drops-158127},
  doi =		{10.4230/LIPIcs.STACS.2022.2},
  annote =	{Keywords: mechanism configuration, algorithm configuration, machine learning, generalization guarantees}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2022.3
Deterministic Distributed Symmetry Breaking at the Example of Distributed Graph Coloring (Invited Talk)

Authors: Fabian Kuhn

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
The problem of obtaining fast deterministic algorithms for distributed symmetry breaking problems in graphs has long been considered one of the most challenging problems in the area of distributed graph algorithms. Consider for example the distributed coloring problem, where a (computer) network is modeled by an arbitrary graph G = (V,E) and the objective is to compute a vertex coloring of G by running a distributed algorithm on the graph G. It is maybe not surprising that randomization can be a helpful tool to efficiently compute such a coloring. In fact, as long as each node v ∈ V can choose among deg(v)+1 different colors, even an almost trivial algorithm in which all nodes keep trying a random available color allows to color all nodes in O(log n) parallel steps. How to obtain a similarly efficient deterministic distributed coloring algorithm is far less obvious. In fact, for a long time, there has been an exponential gap between the time complexities of the best randomized and the best deterministic distributed algorithms for various graph coloring variants and for many other basic graph problems. In the last few years, there however has been substantial progress on deterministic distributed graph algorithms that are nearly as fast as randomized algorithms for the same tasks. In particular, in a recent breakthrough, Rozhoň and Ghaffari managed to reduce the gap between the randomized and deterministic complexities of locally checkable graph problems to at most polylog n. In the talk, we give a brief overview of the history of the problem of finding fast deterministic algorithms for distributed symmetry breaking problems and of what we know about the relation between deterministic and randomized distributed algorithms for such problems. Together with some additional recent developments, the result of Rozhoň and Ghaffari provides a generic, somewhat brute-force way to efficiently derandomize randomized distributed algorithms. Apart from this, there has also been substantial progress on more direct, problem-specific algorithms. In the talk, we in particular discuss some novel deterministic distributed graph coloring algorithms. The algorithms are signficantly faster and we believe also simpler than previous algorithms for the same coloring problems.
Cite as

Fabian Kuhn. Deterministic Distributed Symmetry Breaking at the Example of Distributed Graph Coloring (Invited Talk). In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kuhn:LIPIcs.STACS.2022.3,
  author =	{Kuhn, Fabian},
  title =	{{Deterministic Distributed Symmetry Breaking at the Example of Distributed Graph Coloring}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.3},
  URN =		{urn:nbn:de:0030-drops-158131},
  doi =		{10.4230/LIPIcs.STACS.2022.3},
  annote =	{Keywords: distributed graph algorithms, derandomization, distributed coloring}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.4
Mapping Networks via Parallel kth-Hop Traceroute Queries

Authors: Ramtin Afshar, Michael T. Goodrich, Pedro Matias, and Martha C. Osegueda

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
For a source node, v, and target node, w, the traceroute command iteratively issues "kth-hop" queries, for k = 1, 2, … , δ(v,w), which return the name of the kth vertex on a shortest path from v to w, where δ(v,w) is the distance between v and w, that is, the number of edges in a shortest-path from v to w. The traceroute command is often used for network mapping applications, the study of the connectivity of networks, and it has been studied theoretically with respect to biases it introduces for network mapping when only a subset of nodes in the network can be the source of traceroute queries. In this paper, we provide efficient network mapping algorithms, that are based on kth-hop traceroute queries. Our results include an algorithm that runs in a constant number of parallel rounds with a subquadratic number of queries under reasonable assumptions about the sampling coverage of the nodes that may issue kth-hop traceroute queries. In addition, we introduce a number of new algorithmic techniques, including a high-probability parametric parallelization of a graph clustering technique of Thorup and Zwick, which may be of independent interest.
Cite as

Ramtin Afshar, Michael T. Goodrich, Pedro Matias, and Martha C. Osegueda. Mapping Networks via Parallel kth-Hop Traceroute Queries. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 4:1-4:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{afshar_et_al:LIPIcs.STACS.2022.4,
  author =	{Afshar, Ramtin and Goodrich, Michael T. and Matias, Pedro and Osegueda, Martha C.},
  title =	{{Mapping Networks via Parallel kth-Hop Traceroute Queries}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{4:1--4:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.4},
  URN =		{urn:nbn:de:0030-drops-158142},
  doi =		{10.4230/LIPIcs.STACS.2022.4},
  annote =	{Keywords: Network mapping, graph algorithms, parallel algorithms, distributed computing, query complexity, kth-hop queries}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.5
On Robustness for the Skolem and Positivity Problems

Authors: S. Akshay, Hugo Bazille, Blaise Genest, and Mihir Vahanwala

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
The Skolem problem is a long-standing open problem in linear dynamical systems: can a linear recurrence sequence (LRS) ever reach 0 from a given initial configuration? Similarly, the positivity problem asks whether the LRS stays positive from an initial configuration. Deciding Skolem (or positivity) has been open for half a century: The best known decidability results are for LRS with special properties (e.g., low order recurrences). On the other hand, these problems are much easier for "uninitialized" variants, where the initial configuration is not fixed but can vary arbitrarily: checking if there is an initial configuration from which the LRS stays positive can be decided by polynomial time algorithms (Tiwari in 2004, Braverman in 2006). In this paper, we consider problems that lie between the initialized and uninitialized variant. More precisely, we ask if 0 (resp. negative numbers) can be avoided from every initial configuration in a neighborhood of a given initial configuration. This can be considered as a robust variant of the Skolem (resp. positivity) problem. We show that these problems lie at the frontier of decidability: if the neighborhood is given as part of the input, then robust Skolem and robust positivity are Diophantine-hard, i.e., solving either would entail major breakthrough in Diophantine approximations, as happens for (non-robust) positivity. Interestingly, this is the first Diophantine-hardness result on a variant of the Skolem problem, to the best of our knowledge. On the other hand, if one asks whether such a neighborhood exists, then the problems turn out to be decidable in their full generality, with PSPACE complexity. Our analysis is based on the set of initial configurations such that positivity holds, which leads to new insights into these difficult problems, and interesting geometrical interpretations.
Cite as

S. Akshay, Hugo Bazille, Blaise Genest, and Mihir Vahanwala. On Robustness for the Skolem and Positivity Problems. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{akshay_et_al:LIPIcs.STACS.2022.5,
  author =	{Akshay, S. and Bazille, Hugo and Genest, Blaise and Vahanwala, Mihir},
  title =	{{On Robustness for the Skolem and Positivity Problems}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.5},
  URN =		{urn:nbn:de:0030-drops-158156},
  doi =		{10.4230/LIPIcs.STACS.2022.5},
  annote =	{Keywords: Skolem problem, verification, dynamical systems, robustness}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.6
Approximability of Robust Network Design: The Directed Case

Authors: Yacine Al-Najjar, Walid Ben-Ameur, and Jérémie Leguay

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
We consider robust network design problems where an uncertain traffic vector belonging to a polytope has to be dynamically routed to minimize either the network congestion or some linear reservation cost. We focus on the variant in which the underlying graph is directed. We prove that an O(√k) = O(n)-approximation can be obtained by solving the problem under static routing, where k is the number of commodities and n is the number of nodes. This improves previous results of Hajiaghayi et al. [SODA'2005] and matches the Ω(n) lower bound of Ene et al. [STOC'2016] and the Ω(√k) lower bound of Azar et al. [STOC'2003]. Finally, we introduce a slightly more general problem version where some flow restrictions can be added. We show that it cannot be approximated within a ratio of k^{c/(log log k)} (resp. n^{c/(log log n)}) for some constant c. Making use of a weaker complexity assumption, we prove that there is no approximation within a factor of 2^{log^{1- ε} k} (resp. 2^{log^{1- ε} n}) for any ε > 0.
Cite as

Yacine Al-Najjar, Walid Ben-Ameur, and Jérémie Leguay. Approximability of Robust Network Design: The Directed Case. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{alnajjar_et_al:LIPIcs.STACS.2022.6,
  author =	{Al-Najjar, Yacine and Ben-Ameur, Walid and Leguay, J\'{e}r\'{e}mie},
  title =	{{Approximability of Robust Network Design: The Directed Case}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.6},
  URN =		{urn:nbn:de:0030-drops-158165},
  doi =		{10.4230/LIPIcs.STACS.2022.6},
  annote =	{Keywords: Robust Optimization, Network Design, Approximation, Inapproximability, Competitive Ratio of Oblivious Routing}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.7
Existential Definability over the Subword Ordering

Authors: Pascal Baumann, Moses Ganardi, Ramanathan S. Thinniyam, and Georg Zetzsche

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
We study first-order logic (FO) over the structure consisting of finite words over some alphabet A, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is well-understood: If every word is available as a constant, then even the Σ₁ (i.e., existential) fragment is undecidable, already for binary alphabets A. However, up to now, little is known about the expressiveness of the quantifier alternation fragments: For example, the undecidability proof for the existential fragment relies on Diophantine equations and only shows that recursively enumerable languages over a singleton alphabet (and some auxiliary predicates) are definable. We show that if |A| ≥ 3, then a relation is definable in the existential fragment over A with constants if and only if it is recursively enumerable. This implies characterizations for all fragments Σ_i: If |A| ≥ 3, then a relation is definable in Σ_i if and only if it belongs to the i-th level of the arithmetical hierarchy. In addition, our result yields an analogous complete description of the Σ_i-fragments for i ≥ 2 of the pure logic, where the words of A^* are not available as constants.
Cite as

Pascal Baumann, Moses Ganardi, Ramanathan S. Thinniyam, and Georg Zetzsche. Existential Definability over the Subword Ordering. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{baumann_et_al:LIPIcs.STACS.2022.7,
  author =	{Baumann, Pascal and Ganardi, Moses and Thinniyam, Ramanathan S. and Zetzsche, Georg},
  title =	{{Existential Definability over the Subword Ordering}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.7},
  URN =		{urn:nbn:de:0030-drops-158178},
  doi =		{10.4230/LIPIcs.STACS.2022.7},
  annote =	{Keywords: subword, subsequence, definability, expressiveness, first order logic, existential fragment, quantifier alternation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.8
Intrinsic Complexity of Recursive Functions on Natural Numbers with Standard Order

Authors: Nikolay Bazhenov, Dariusz Kalociński, and Michał Wrocławski

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
The intrinsic complexity of a relation on a given computable structure is captured by the notion of its degree spectrum - the set of Turing degrees of images of the relation in all computable isomorphic copies of that structure. We investigate the intrinsic complexity of unary total recursive functions on nonnegative integers with standard order. According to existing results, the possible spectra of such functions include three sets consisting of precisely: the computable degree, all c.e. degrees and all Δ₂ degrees. These results, however, fall far short of the full classification. In this paper, we obtain a more complete picture by giving a few criteria for a function to have intrinsic complexity equal to one of the three candidate sets of degrees. Our investigations are based on the notion of block functions and a broader class of quasi-block functions beyond which all functions of interest have intrinsic complexity equal to the c.e. degrees. We also answer the questions raised by Wright [Wright, 2018] and Harrison-Trainor [Harrison-Trainor, 2018] by showing that the division between computable, c.e. and Δ₂ degrees is insufficient in this context as there is a unary total recursive function whose spectrum contains all c.e. degrees but is strictly contained in the Δ₂ degrees.
Cite as

Nikolay Bazhenov, Dariusz Kalociński, and Michał Wrocławski. Intrinsic Complexity of Recursive Functions on Natural Numbers with Standard Order. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bazhenov_et_al:LIPIcs.STACS.2022.8,
  author =	{Bazhenov, Nikolay and Kaloci\'{n}ski, Dariusz and Wroc{\l}awski, Micha{\l}},
  title =	{{Intrinsic Complexity of Recursive Functions on Natural Numbers with Standard Order}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.8},
  URN =		{urn:nbn:de:0030-drops-158185},
  doi =		{10.4230/LIPIcs.STACS.2022.8},
  annote =	{Keywords: Computable Structure Theory, Degree Spectra, \omega-Type Order, c.e. Degrees, d.c.e. Degrees, \Delta₂ Degrees, Learnability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.9
Subquadratic-Time Algorithm for the Diameter and All Eccentricities on Median Graphs

Authors: Pierre Bergé, Guillaume Ducoffe, and Michel Habib

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
On sparse graphs, Roditty and Williams [2013] proved that no O(n^{2-ε})-time algorithm achieves an approximation factor smaller than 3/2 for the diameter problem unless SETH fails. We answer here an open question formulated in the literature: can we use the structural properties of median graphs to break this global quadratic barrier? We propose the first combinatorial algorithm computing exactly all eccentricities of a median graph in truly subquadratic time. Median graphs constitute the family of graphs which is the most studied in metric graph theory because their structure represents many other discrete and geometric concepts, such as CAT(0) cube complexes. Our result generalizes a recent one, stating that there is a linear-time algorithm for computing all eccentricities in median graphs with bounded dimension d, i.e. the dimension of the largest induced hypercube (note that 1-dimensional median graphs are exactly the forests). This prerequisite on d is not necessarily anymore to determine all eccentricities in subquadratic time. The execution time of our algorithm is O(n^{1.6456}log^{O(1)} n).
Cite as

Pierre Bergé, Guillaume Ducoffe, and Michel Habib. Subquadratic-Time Algorithm for the Diameter and All Eccentricities on Median Graphs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{berge_et_al:LIPIcs.STACS.2022.9,
  author =	{Berg\'{e}, Pierre and Ducoffe, Guillaume and Habib, Michel},
  title =	{{Subquadratic-Time Algorithm for the Diameter and All Eccentricities on Median Graphs}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.9},
  URN =		{urn:nbn:de:0030-drops-158192},
  doi =		{10.4230/LIPIcs.STACS.2022.9},
  annote =	{Keywords: Diameter, Eccentricities, Metric graph theory, Median graphs, Hypercubes}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.10
Faster Counting and Sampling Algorithms Using Colorful Decision Oracle

Authors: Anup Bhattacharya, Arijit Bishnu, Arijit Ghosh, and Gopinath Mishra

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
In this work, we consider d-Hyperedge Estimation and d-Hyperedge Sample problem in a hypergraph H(U(H),F(H)) in the query complexity framework, where U(H) denotes the set of vertices and F(H) denotes the set of hyperedges. The oracle access to the hypergraph is called Colorful Independence Oracle (CID), which takes d (non-empty) pairwise disjoint subsets of vertices A₁,…, A_d ⊆ U(ℋ) as input, and answers whether there exists a hyperedge in H having (exactly) one vertex in each A_i, i ∈ {1,2,…,d}. The problem of d-Hyperedge Estimation and d-Hyperedge Sample with CID oracle access is important in its own right as a combinatorial problem. Also, Dell et al. [SODA '20] established that decision vs counting complexities of a number of combinatorial optimization problems can be abstracted out as d-Hyperedge Estimation problems with a CID oracle access. The main technical contribution of the paper is an algorithm that estimates m = |F(H)| with m̂ such that 1/(C_{d)log^{d-1} n) ≤ m̂/m ≤ C_{d} log ^{d-1} n. by using at most C_{d}log ^{d+2} n many CID queries, where n denotes the number of vertices in the hypergraph H and C_d is a constant that depends only on d}. Our result coupled with the framework of Dell et al. [SODA '21] implies improved bounds for the following fundamental problems: Edge Estimation using the Bipartite Independent Set (BIS). We improve the bound obtained by Beame et al. [ITCS '18, TALG '20]. Triangle Estimation using the Tripartite Independent Set (TIS). The previous best bound for the case of graphs with low co-degree (Co-degree for an edge in the graph is the number of triangles incident to that edge in the graph) was due to Bhattacharya et al. [ISAAC '19, TOCS '21], and Dell {et al.}’s result gives the best bound for the case of general graphs [SODA '21]. We improve both of these bounds. Hyperedge Estimation & Sampling using Colorful Independence Oracle (CID). We give an improvement over the bounds obtained by Dell et al. [SODA '21].
Cite as

Anup Bhattacharya, Arijit Bishnu, Arijit Ghosh, and Gopinath Mishra. Faster Counting and Sampling Algorithms Using Colorful Decision Oracle. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bhattacharya_et_al:LIPIcs.STACS.2022.10,
  author =	{Bhattacharya, Anup and Bishnu, Arijit and Ghosh, Arijit and Mishra, Gopinath},
  title =	{{Faster Counting and Sampling Algorithms Using Colorful Decision Oracle}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.10},
  URN =		{urn:nbn:de:0030-drops-158205},
  doi =		{10.4230/LIPIcs.STACS.2022.10},
  annote =	{Keywords: Query Complexity, Subset Query, Hyperedge Estimation, and Colorful Independent Set oracle}
}
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