License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SWAT.2016.18
URN: urn:nbn:de:0030-drops-60405
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6040/
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Kolman, Petr ; Koutecký, Martin ; Tiwary, Hans Raj

Extension Complexity, MSO Logic, and Treewidth

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LIPIcs-SWAT-2016-18.pdf (0.5 MB)

Abstract

We consider the convex hull P_phi(G) of all satisfying assignments of a given MSO_2 formula phi on a given graph G. We show that there exists an extended formulation of the polytope P_phi(G) that can be described by f(|phi|,tau)*n inequalities, where n is the number of vertices in G, tau is the treewidth of G and f is a computable function depending only on phi and tau.

In other words, we prove that the extension complexity of P_phi(G) is linear in the size of the graph G, with a constant depending on the treewidth of G and the formula phi. This provides a very general yet very simple meta-theorem about the extension complexity of polytopes related to a wide class of problems and graphs.

BibTeX - Entry

@InProceedings{kolman_et_al:LIPIcs:2016:6040,
  author =	{Petr Kolman and Martin Kouteck{\'y} and Hans Raj Tiwary},
  title =	{{Extension Complexity, MSO Logic, and Treewidth }},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Rasmus Pagh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6040},
  URN =		{urn:nbn:de:0030-drops-60405},
  doi =		{10.4230/LIPIcs.SWAT.2016.18},
  annote =	{Keywords: Extension Complexity, FPT, Courcelle's Theorem, MSO Logic}
}

Keywords: Extension Complexity, FPT, Courcelle's Theorem, MSO Logic
Collection: 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)
Issue Date: 2016
Date of publication: 22.06.2016

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