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DOI: 10.4230/LIPIcs.SWAT.2018.18
URN: urn:nbn:de:0030-drops-88441
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8844/
Elbassioni, Khaled ; Makino, Kazuhisa
Enumerating Vertices of 0/1-Polyhedra associated with 0/1-Totally Unimodular Matrices
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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 | |
| Seminar: | 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 04.06.2018 |
