3 Search Results for "Wollan, Paul"

Document
DOI: 10.4230/LIPIcs.MFCS.2019.49
Bounded-Depth Frege Complexity of Tseitin Formulas for All Graphs

Authors: Nicola Galesi, Dmitry Itsykson, Artur Riazanov, and Anastasia Sofronova

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We prove that there is a constant K such that Tseitin formulas for an undirected graph G requires proofs of size 2^{tw(G)^{Omega(1/d)}} in depth-d Frege systems for d<(K log n)/(log log n), where tw(G) is the treewidth of G. This extends Håstad recent lower bound for the grid graph to any graph. Furthermore, we prove tightness of our bound up to a multiplicative constant in the top exponent. Namely, we show that if a Tseitin formula for a graph G has size s, then for all large enough d, it has a depth-d Frege proof of size 2^{tw(G)^{O(1/d)}} poly(s). Through this result we settle the question posed by M. Alekhnovich and A. Razborov of showing that the class of Tseitin formulas is quasi-automatizable for resolution.
Cite as

Nicola Galesi, Dmitry Itsykson, Artur Riazanov, and Anastasia Sofronova. Bounded-Depth Frege Complexity of Tseitin Formulas for All Graphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 49:1-49:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{galesi_et_al:LIPIcs.MFCS.2019.49,
  author =	{Galesi, Nicola and Itsykson, Dmitry and Riazanov, Artur and Sofronova, Anastasia},
  title =	{{Bounded-Depth Frege Complexity of Tseitin Formulas for All Graphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{49:1--49:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.49},
  URN =		{urn:nbn:de:0030-drops-109932},
  doi =		{10.4230/LIPIcs.MFCS.2019.49},
  annote =	{Keywords: Tseitin formula, treewidth, AC0-Frege}
}
Document
DOI: 10.4230/LIPIcs.STACS.2019.32
Lean Tree-Cut Decompositions: Obstructions and Algorithms

Authors: Archontia C. Giannopoulou, O-joung Kwon, Jean-Florent Raymond, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Abstract
The notion of tree-cut width has been introduced by Wollan in [The structure of graphs not admitting a fixed immersion, Journal of Combinatorial Theory, Series B, 110:47 - 66, 2015]. It is defined via tree-cut decompositions, which are tree-like decompositions that highlight small (edge) cuts in a graph. In that sense, tree-cut decompositions can be seen as an edge-version of tree-decompositions and have algorithmic applications on problems that remain intractable on graphs of bounded treewidth. In this paper, we prove that every graph admits an optimal tree-cut decomposition that satisfies a certain Menger-like condition similar to that of the lean tree decompositions of Thomas [A Menger-like property of tree-width: The finite case, Journal of Combinatorial Theory, Series B, 48(1):67 - 76, 1990]. This allows us to give, for every k in N, an upper-bound on the number immersion-minimal graphs of tree-cut width k. Our results imply the constructive existence of a linear FPT-algorithm for tree-cut width.
Cite as

Archontia C. Giannopoulou, O-joung Kwon, Jean-Florent Raymond, and Dimitrios M. Thilikos. Lean Tree-Cut Decompositions: Obstructions and Algorithms. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{giannopoulou_et_al:LIPIcs.STACS.2019.32,
  author =	{Giannopoulou, Archontia C. and Kwon, O-joung and Raymond, Jean-Florent and Thilikos, Dimitrios M.},
  title =	{{Lean Tree-Cut Decompositions: Obstructions and Algorithms}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{32:1--32:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.32},
  URN =		{urn:nbn:de:0030-drops-102716},
  doi =		{10.4230/LIPIcs.STACS.2019.32},
  annote =	{Keywords: tree-cut width, lean decompositions, immersions, obstructions, parameterized algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.36
Half-Integral Linkages in Highly Connected Directed Graphs

Authors: Katherine Edwards, Irene Muzi, and Paul Wollan

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We study the half-integral k-Directed Disjoint Paths Problem (1/2 kDDPP) in highly strongly connected digraphs. The integral kDDPP is NP-complete even when restricted to instances where k=2, and the input graph is L-strongly connected, for any L >= 1. We show that when the integrality condition is relaxed to allow each vertex to be used in two paths, the problem becomes efficiently solvable in highly connected digraphs (even with k as part of the input). Specifically, we show that there is an absolute constant c such that for each k >= 2 there exists L(k) such that 1/2 kDDPP is solvable in time O(|V(G)|^c) for a L(k)-strongly connected directed graph G. As the function L(k) grows rather quickly, we also show that 1/2 kDDPP is solvable in time O(|V(G)|^{f(k)}) in (36k^3+2k)-strongly connected directed graphs. We show that for each epsilon<1, deciding half-integral feasibility of kDDPP instances is NP-complete when k is given as part of the input, even when restricted to graphs with strong connectivity epsilon k.
Cite as

Katherine Edwards, Irene Muzi, and Paul Wollan. Half-Integral Linkages in Highly Connected Directed Graphs. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 36:1-36:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{edwards_et_al:LIPIcs.ESA.2017.36,
  author =	{Edwards, Katherine and Muzi, Irene and Wollan, Paul},
  title =	{{Half-Integral Linkages in Highly Connected Directed Graphs}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{36:1--36:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.36},
  URN =		{urn:nbn:de:0030-drops-78769},
  doi =		{10.4230/LIPIcs.ESA.2017.36},
  annote =	{Keywords: linkage, directed graph, treewidth}
}
  • Refine by Author
  • 1 Edwards, Katherine
  • 1 Galesi, Nicola
  • 1 Giannopoulou, Archontia C.
  • 1 Itsykson, Dmitry
  • 1 Kwon, O-joung
  • Show More...

  • Refine by Classification
  • 1 Mathematics of computing → Graph algorithms
  • 1 Theory of computation → Computational complexity and cryptography
  • 1 Theory of computation → Fixed parameter tractability

  • Refine by Keyword
  • 2 treewidth
  • 1 AC0-Frege
  • 1 Tseitin formula
  • 1 directed graph
  • 1 immersions
  • Show More...

  • Refine by Type
  • 3 document

  • Refine by Publication Year
  • 2 2019
  • 1 2017

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact