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

2017
*
arXiv
*
pre-print

We give an incremental polynomial time algorithm for

arXiv:1707.03914v1
fatcat:2ir3zoeaxzasrhtnjqn4uim3he
*enumerating*the*vertices**of*any polyhedron P(A,1)={x∈^n | Ax≥1̱, x≥0̱}, 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. ... The research*of*the second author is supported by Grant-in-Aid for Scientific Research 24106002, 25280004, 26280001 and JST CREST Grant Number JPMJCR1402, Japan. ...##
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Enumerating Vertices of 0/1-Polyhedra associated with 0/1-Totally Unimodular Matrices

2018
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Scandinavian Workshop on Algorithm Theory
*

ACM Subject Classification Mathematics

doi:10.4230/lipics.swat.2018.18
dblp:conf/swat/ElbassioniM18
fatcat:gjsdnsp3irhvzod24sdhugbc5m
*of*computing → Combinatorial algorithms, Mathematics*of*computing → Hypergraphs Keywords and phrases Totally*unimodular**matrices*,*Vertices**of*polyhedra, Vertex*enumeration*... We give an incremental polynomial time algorithm for*enumerating*the*vertices**of*any polyhedron A is a totally*unimodular*matrix. ... VE for*0*/*1*-*Polyhedra**Associated**with**0*/*1*-*Totally**Unimodular**Matrices*Let A ∈ {0, 1} m×n be an m × n 0/1-matrix such that the polyhedron P(A, 1 ¯) = {x ∈ R n | Ax ≥ 1 ¯, x ≥ 0 ¯} (1) has only integral*vertices*...