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

Khaled Elbassioni, Kazuhisa Makino
2017 arXiv   pre-print
We give an incremental polynomial time algorithm for 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.  ... 
arXiv:1707.03914v1 fatcat:2ir3zoeaxzasrhtnjqn4uim3he

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

Khaled Elbassioni, Kazuhisa Makino, Marc Herbstritt
2018 Scandinavian Workshop on Algorithm Theory  
ACM Subject Classification Mathematics 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  ... 
doi:10.4230/lipics.swat.2018.18 dblp:conf/swat/ElbassioniM18 fatcat:gjsdnsp3irhvzod24sdhugbc5m