167 Search Results for "Paul, Christophe"


Volume

LIPIcs, Volume 154

37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

STACS 2020, March 10-13, 2020, Montpellier, France

Editors: Christophe Paul and Markus Bläser

Volume

LIPIcs, Volume 126

36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

STACS 2019, March 13-16, 2019, Berlin, Germany

Editors: Rolf Niedermeier and Christophe Paul

Volume

LIPIcs, Volume 115

13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

IPEC 2018, August 20-24, 2018, Helsinki, Finland

Editors: Christophe Paul and Michal Pilipczuk

Document
Tree-Layout Based Graph Classes: Proper Chordal Graphs

Authors: Christophe Paul and Evangelos Protopapas

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)


Abstract
Many important graph classes are characterized by means of layouts (a vertex ordering) excluding some patterns. For example, a graph G = (V,E) is a proper interval graph if and only if G has a layout 𝐋 such that for every triple of vertices such that x≺_𝐋 y≺_𝐋 z, if xz ∈ E, then xy ∈ E and yz ∈ E. Such a triple x, y, z is called an indifference triple. In this paper, we investigate the concept of excluding a set of patterns in tree-layouts rather than layouts. A tree-layout 𝐓_G = (T,r,ρ_G) of a graph G = (V,E) is a tree T rooted at some node r and equipped with a one-to-one mapping ρ_G between V and the nodes of T such that for every edge xy ∈ E, either x is an ancestor of y, denoted x≺_{𝐓_G} y, or y is an ancestor of x. Excluding patterns in a tree-layout is now defined using the ancestor relation. This leads to an unexplored territory of graph classes. In this paper, we initiate the study of such graph classes with the class of proper chordal graphs defined by excluding indifference triples in tree-layouts. Our results combine characterization, compact and canonical representation as well as polynomial time algorithms for the recognition and the graph isomorphism of proper chordal graphs. For this, one of the key ingredients is the introduction of the concept of FPQ-hierarchy generalizing the celebrated PQ-tree data-structure.

Cite as

Christophe Paul and Evangelos Protopapas. Tree-Layout Based Graph Classes: Proper Chordal Graphs. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 55:1-55:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{paul_et_al:LIPIcs.STACS.2024.55,
  author =	{Paul, Christophe and Protopapas, Evangelos},
  title =	{{Tree-Layout Based Graph Classes: Proper Chordal Graphs}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{55:1--55:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.55},
  URN =		{urn:nbn:de:0030-drops-197652},
  doi =		{10.4230/LIPIcs.STACS.2024.55},
  annote =	{Keywords: Graph classes, Graph representation, Graph isomorphism}
}
Document
Treewidth-Based Algorithms for the Small Parsimony Problem on Networks

Authors: Celine Scornavacca and Mathias Weller

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)


Abstract
Phylogenetic reconstruction is one of the paramount challenges of contemporary bioinformatics. A subtask of existing tree reconstruction algorithms is modeled by the Small Parsimony problem: given a tree T and an assignment of character-states to its leaves, assign states to the internal nodes of T such as to minimize the parsimony score, that is, the number of edges of T connecting nodes with different states. While this problem is polynomial-time solvable on trees, the matter is more complicated if T contains reticulate events such as hybridizations or recombinations, i.e. when T is a network. Indeed, three different versions of the parsimony score on networks have been proposed and each of them is NP-hard to decide. Existing parameterized algorithms focus on combining the number of possible character-states with the number of reticulate events (per biconnected component). Here, we consider the treewidth of the undirected graph underlying the input network as parameter, presenting dynamic programming algorithms for (slight generalizations of) all three versions of the parsimony problem on networks. Our algorithms use a formulation of the treewidth that may facilitate formalizing treewidth-based dynamic programming algorithms on phylogenetic networks for other problems.

Cite as

Celine Scornavacca and Mathias Weller. Treewidth-Based Algorithms for the Small Parsimony Problem on Networks. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{scornavacca_et_al:LIPIcs.WABI.2021.6,
  author =	{Scornavacca, Celine and Weller, Mathias},
  title =	{{Treewidth-Based Algorithms for the Small Parsimony Problem on Networks}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{6:1--6:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.6},
  URN =		{urn:nbn:de:0030-drops-143591},
  doi =		{10.4230/LIPIcs.WABI.2021.6},
  annote =	{Keywords: Phylogenetics, parsimony, phylogenetic networks, parameterized complexity, dynamic programming, treewidth}
}
Document
Short Paper
Proof of Behavior (Short Paper)

Authors: Paul-Marie Grollemund, Pascal Lafourcade, Kevin Thiry-Atighehchi, and Ariane Tichit

Published in: OASIcs, Volume 82, 2nd International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2020)


Abstract
Our aim is to change the Proof of Work paradigm. Instead of wasting energy in dummy computations with hash computations, we propose a new approach based on the behavior of the users. Our idea is to design a mechanism that replaces the Proof of Work and that has a positive impact on the world and a social impact on the behaviors of the citizens. For this, we introduce the notion of Proof of Behavior. Based on this notion, we present a new cryptocurrency, called EcoMobiCoin, that encourages the ecological behavior in the mobility of the citizens.

Cite as

Paul-Marie Grollemund, Pascal Lafourcade, Kevin Thiry-Atighehchi, and Ariane Tichit. Proof of Behavior (Short Paper). In 2nd International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2020). Open Access Series in Informatics (OASIcs), Volume 82, pp. 11:1-11:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{grollemund_et_al:OASIcs.Tokenomics.2020.11,
  author =	{Grollemund, Paul-Marie and Lafourcade, Pascal and Thiry-Atighehchi, Kevin and Tichit, Ariane},
  title =	{{Proof of Behavior}},
  booktitle =	{2nd International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2020)},
  pages =	{11:1--11:6},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-157-3},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{82},
  editor =	{Anceaume, Emmanuelle and Bisi\`{e}re, Christophe and Bouvard, Matthieu and Bramas, Quentin and Casamatta, Catherine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.Tokenomics.2020.11},
  URN =		{urn:nbn:de:0030-drops-135330},
  doi =		{10.4230/OASIcs.Tokenomics.2020.11},
  annote =	{Keywords: Proof of behavior, Blockchain, Security}
}
Document
A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth

Authors: Mamadou Moustapha Kanté, Christophe Paul, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)


Abstract
The graph parameter of pathwidth can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of node search where we are given a system of tunnels (represented by a graph) that is contaminated by some infectious substance and we are looking for a search strategy that, at each step, either places a searcher on a vertex or removes a searcher from a vertex and where an edge is cleaned when both endpoints are simultaneously occupied by searchers. It was proved that the minimum number of searchers required for a successful cleaning strategy is equal to the pathwidth of the graph plus one. Two desired characteristics for a cleaning strategy is to be monotone (no recontamination occurs) and connected (clean territories always remain connected). Under these two demands, the number of searchers is equivalent to a variant of pathwidth called connected pathwidth. We prove that connected pathwidth is fixed parameter tractable, in particular we design a 2^O(k²)⋅n time algorithm that checks whether the connected pathwidth of G is at most k. This resolves an open question by [Dereniowski, Osula, and Rzążewski, Finding small-width connected path-decompositions in polynomial time. Theor. Comput. Sci., 794:85–100, 2019]. For our algorithm, we enrich the typical sequence technique that is able to deal with the connectivity demand. Typical sequences have been introduced in [Bodlaender and Kloks. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms, 21(2):358–402, 1996] for the design of linear parameterized algorithms for treewidth and pathwidth. While this technique has been later applied to other parameters, none of its advancements was able to deal with the connectivity demand, as it is a "global" demand that concerns an unbounded number of parts of the graph of unbounded size. The proposed extension is based on an encoding of the connectivity property that is quite versatile and may be adapted so to deliver linear parameterized algorithms for the connected variants of other width parameters as well. An immediate consequence of our result is a 2^O(k²)⋅n time algorithm for the monotone and connected version of the edge search number.

Cite as

Mamadou Moustapha Kanté, Christophe Paul, and Dimitrios M. Thilikos. A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{kante_et_al:LIPIcs.ESA.2020.64,
  author =	{Kant\'{e}, Mamadou Moustapha and Paul, Christophe and Thilikos, Dimitrios M.},
  title =	{{A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.64},
  URN =		{urn:nbn:de:0030-drops-129307},
  doi =		{10.4230/LIPIcs.ESA.2020.64},
  annote =	{Keywords: Graph decompositions, Parameterized algorithms, Typical sequences, Pathwidth, Graph searching}
}
Document
Hierarchical Clusterings of Unweighted Graphs

Authors: Svein Høgemo, Christophe Paul, and Jan Arne Telle

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)


Abstract
We study the complexity of finding an optimal hierarchical clustering of an unweighted similarity graph under the recently introduced Dasgupta objective function. We introduce a proof technique, called the normalization procedure, that takes any such clustering of a graph G and iteratively improves it until a desired target clustering of G is reached. We use this technique to show both a negative and a positive complexity result. Firstly, we show that in general the problem is NP-complete. Secondly, we consider min-well-behaved graphs, which are graphs H having the property that for any k the graph H^{(k)} being the join of k copies of H has an optimal hierarchical clustering that splits each copy of H in the same optimal way. To optimally cluster such a graph H^{(k)} we thus only need to optimally cluster the smaller graph H. Co-bipartite graphs are min-well-behaved, but otherwise they seem to be scarce. We use the normalization procedure to show that also the cycle on 6 vertices is min-well-behaved.

Cite as

Svein Høgemo, Christophe Paul, and Jan Arne Telle. Hierarchical Clusterings of Unweighted Graphs. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 47:1-47:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{hgemo_et_al:LIPIcs.MFCS.2020.47,
  author =	{H{\o}gemo, Svein and Paul, Christophe and Telle, Jan Arne},
  title =	{{Hierarchical Clusterings of Unweighted Graphs}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{47:1--47:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.47},
  URN =		{urn:nbn:de:0030-drops-127139},
  doi =		{10.4230/LIPIcs.MFCS.2020.47},
  annote =	{Keywords: Hierarchical Clustering}
}
Document
Complete Volume
LIPIcs, Vol. 154, STACS 2020, Complete Volume

Authors: Christophe Paul and Markus Bläser

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
LIPIcs, Vol. 154, STACS 2020, Complete Volume

Cite as

37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 0-1024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@Proceedings{paul_et_al:LIPIcs.STACS.2020,
  title =	{{LIPIcs, Vol. 154, STACS 2020, Complete Volume}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020},
  URN =		{urn:nbn:de:0030-drops-118603},
  doi =		{10.4230/LIPIcs.STACS.2020},
  annote =	{Keywords: LIPIcs, Vol. 154, STACS 2020, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Christophe Paul and Markus Bläser

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


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

Cite as

37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{paul_et_al:LIPIcs.STACS.2020.0,
  author =	{Paul, Christophe and Bl\"{a}ser, Markus},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.0},
  URN =		{urn:nbn:de:0030-drops-118614},
  doi =		{10.4230/LIPIcs.STACS.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
Statistical Physics and Algorithms (Invited Talk)

Authors: Dana Randall

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
The field of randomized algorithms has benefitted greatly from insights from statistical physics. We give examples in two distinct settings. The first is in the context of Markov chain Monte Carlo algorithms, which have become ubiquitous across science and engineering as a means of exploring large configuration spaces. One of the most striking discoveries was the realization that many natural Markov chains undergo phase transitions, whereby they are efficient for some parameter settings and then suddenly become inefficient as a parameter of the system is slowly modified. The second is in the context of distributed algorithms for programmable matter. Self-organizing particle systems based on statistical models with phase changes have been used to achieve basic tasks involving coordination, movement, and conformation in a fully distributed, local setting. We briefly describe these two settings to demonstrate how computing and statistical physics together provide powerful insights that apply across multiple domains.

Cite as

Dana Randall. Statistical Physics and Algorithms (Invited Talk). In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 1:1-1:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{randall:LIPIcs.STACS.2020.1,
  author =	{Randall, Dana},
  title =	{{Statistical Physics and Algorithms}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{1:1--1:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.1},
  URN =		{urn:nbn:de:0030-drops-118624},
  doi =		{10.4230/LIPIcs.STACS.2020.1},
  annote =	{Keywords: Markov chains, mixing times, phase transitions, programmable matter}
}
Document
Invited Talk
Weisfeiler and Leman’s Unlikely Journey from Graph Isomorphism to Neural Networks (Invited Talk)

Authors: Martin Grohe

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
The Weisfeiler-Leman algorithm is a well-known combinatorial graph isomorphism test going back to work of Weisfeiler and Leman in the late 1960s. The algorithm has a surprising number of seemingly unrelated characterisations in terms of logic, algebra, linear and semi-definite programming, and graph homomorphisms. Due to its simplicity and efficiency, it is an important subroutine of all modern graph isomorphism tools. In recent years, further applications in linear optimisation, probabilistic inference, and machine learning have surfaced. In the first part of my talk, I will give an introduction to the Weisfeiler-Leman algorithm and its various characterisations. In the second part I will speak about its applications, in particular about recent work relating the algorithm to graph neural networks.

Cite as

Martin Grohe. Weisfeiler and Leman’s Unlikely Journey from Graph Isomorphism to Neural Networks (Invited Talk). In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{grohe:LIPIcs.STACS.2020.2,
  author =	{Grohe, Martin},
  title =	{{Weisfeiler and Leman’s Unlikely Journey from Graph Isomorphism to Neural Networks}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.2},
  URN =		{urn:nbn:de:0030-drops-118634},
  doi =		{10.4230/LIPIcs.STACS.2020.2},
  annote =	{Keywords: Weisfeiler adn Leman algorithm, Graph isomorphism, Neural network, logic, algebra, linear and semi-definite programming}
}
Document
Invited Talk
Computability, Complexity and Programming with Ordinary Differential Equations (Invited Talk)

Authors: Olivier Bournez

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
Ordinary Differential Equations (ODEs) appear to be a universally adopted and very natural way for expressing properties for continuous time dynamical systems. They are intensively used, in particular in applied sciences. There exists an abundant literature about the hardness of solving ODEs with numerical methods. We adopt a dual view: we consider ODEs as a way to program or to describe our mathematical/computer science world. We survey several results considering ODEs under this computational perspective, with a computability and complexity theory point of view. In particular, we provide various reasons why polynomial ODEs should be considered as the continuous time analog of Turing machines for continuous-time computations, or should be used as a way to talk about mathematical logic. This has already applications in various fields: determining whether analog models of computation can compute faster than classical digital models of computation; solving complexity issues for computations with biochemical reactions in bioinformatics; machine independent characterizations of various computability and complexity classes such as PTIME or NPTIME, or proof of the existence of a universal polynomial ordinary differential equation whose solutions can approximate any continuous function if provided with a suitable well-chosen initial condition.

Cite as

Olivier Bournez. Computability, Complexity and Programming with Ordinary Differential Equations (Invited Talk). In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 3:1-3:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bournez:LIPIcs.STACS.2020.3,
  author =	{Bournez, Olivier},
  title =	{{Computability, Complexity and Programming with Ordinary Differential Equations}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{3:1--3:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.3},
  URN =		{urn:nbn:de:0030-drops-118642},
  doi =		{10.4230/LIPIcs.STACS.2020.3},
  annote =	{Keywords: Ordinary differential equations, Models of computation, Analog Computations, discrete ordinary differential equations, Implicit complexity, recursion scheme}
}
Document
Tutorial
Graphical Models: Queries, Complexity, Algorithms (Tutorial)

Authors: Martin C. Cooper, Simon de Givry, and Thomas Schiex

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
Graphical models (GMs) define a family of mathematical models aimed at the concise description of multivariate functions using decomposability. We restrict ourselves to functions of discrete variables but try to cover a variety of models that are not always considered as "Graphical Models", ranging from functions with Boolean variables and Boolean co-domain (used in automated reasoning) to functions over finite domain variables and integer or real co-domains (usual in machine learning and statistics). We use a simple algebraic semi-ring based framework for generality, define associated queries, relationships between graphical models, complexity results, and families of algorithms, with their associated guarantees.

Cite as

Martin C. Cooper, Simon de Givry, and Thomas Schiex. Graphical Models: Queries, Complexity, Algorithms (Tutorial). In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{cooper_et_al:LIPIcs.STACS.2020.4,
  author =	{Cooper, Martin C. and de Givry, Simon and Schiex, Thomas},
  title =	{{Graphical Models: Queries, Complexity, Algorithms}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.4},
  URN =		{urn:nbn:de:0030-drops-118654},
  doi =		{10.4230/LIPIcs.STACS.2020.4},
  annote =	{Keywords: Computational complexity, tree decomposition, graphical models, submodularity, message passing, local consistency, artificial intelligence, valued constraints, optimization}
}
Document
Inapproximability Results for Scheduling with Interval and Resource Restrictions

Authors: Marten Maack and Klaus Jansen

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
In the restricted assignment problem, the input consists of a set of machines and a set of jobs each with a processing time and a subset of eligible machines. The goal is to find an assignment of the jobs to the machines minimizing the makespan, that is, the maximum summed up processing time any machine receives. Herein, jobs should only be assigned to those machines on which they are eligible. It is well-known that there is no polynomial time approximation algorithm with an approximation guarantee of less than 1.5 for the restricted assignment problem unless P=NP. In this work, we show hardness results for variants of the restricted assignment problem with particular types of restrictions. For the case of interval restrictions - where the machines can be totally ordered such that jobs are eligible on consecutive machines - we show that there is no polynomial time approximation scheme (PTAS) unless P=NP. The question of whether a PTAS for this variant exists was stated as an open problem before, and PTAS results for special cases of this variant are known. Furthermore, we consider a variant with resource restriction where the sets of eligible machines are of the following form: There is a fixed number of (renewable) resources, each machine has a capacity, and each job a demand for each resource. A job is eligible on a machine if its demand is at most as big as the capacity of the machine for each resource. For one resource, this problem has been intensively studied under several different names and is known to admit a PTAS, and for two resources the variant with interval restrictions is contained as a special case. Moreover, the version with multiple resources is closely related to makespan minimization on parallel machines with a low rank processing time matrix. We show that there is no polynomial time approximation algorithm with a rate smaller than 48/47 ≈ 1.02 or 1.5 for scheduling with resource restrictions with 2 or 4 resources, respectively, unless P=NP. All our results can be extended to the so called Santa Claus variants of the problems where the goal is to maximize the minimal processing time any machine receives.

Cite as

Marten Maack and Klaus Jansen. Inapproximability Results for Scheduling with Interval and Resource Restrictions. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{maack_et_al:LIPIcs.STACS.2020.5,
  author =	{Maack, Marten and Jansen, Klaus},
  title =	{{Inapproximability Results for Scheduling with Interval and Resource Restrictions}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.5},
  URN =		{urn:nbn:de:0030-drops-118663},
  doi =		{10.4230/LIPIcs.STACS.2020.5},
  annote =	{Keywords: Scheduling, Restricted Assignment, Approximation, Inapproximability, PTAS}
}
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