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.2018.18
URN: urn:nbn:de:0030-drops-88441
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8844/
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Elbassioni, Khaled ; Makino, Kazuhisa

Enumerating Vertices of 0/1-Polyhedra associated with 0/1-Totally Unimodular Matrices

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LIPIcs-SWAT-2018-18.pdf (0.5 MB)


Abstract

We give an incremental polynomial time algorithm for enumerating the vertices of any polyhedron P=P(A,1_)={x in R^n | Ax >= 1_, x >= 0_}, when A is a totally unimodular matrix. Our algorithm is based on decomposing the hypergraph transversal problem for unimodular hypergraphs using Seymour's decomposition of totally unimodular matrices, and may be of independent interest.

BibTeX - Entry

@InProceedings{elbassioni_et_al:LIPIcs:2018:8844,
  author =	{Khaled Elbassioni and Kazuhisa Makino},
  title =	{{Enumerating Vertices of 0/1-Polyhedra associated with 0/1-Totally Unimodular Matrices}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm  Theory (SWAT 2018)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{David Eppstein},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8844},
  URN =		{urn:nbn:de:0030-drops-88441},
  doi =		{10.4230/LIPIcs.SWAT.2018.18},
  annote =	{Keywords: Totally unimodular matrices, Vertices of polyhedra, Vertex enumeration, Hypergraph transversals, Hypergraph decomposition, Output polynomial-time algo}
}

Keywords: Totally unimodular matrices, Vertices of polyhedra, Vertex enumeration, Hypergraph transversals, Hypergraph decomposition, Output polynomial-time algo
Collection: 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)
Issue Date: 2018
Date of publication: 04.06.2018


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