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The Cartographer
Enumerating Vertices of $0/1$-Polyhedra associated with $0/1$-Totally Unimodular Matrices
July 12, 2017 Β· Declared Dead Β· π Scandinavian Workshop on Algorithm Theory
"No code URL or promise found in abstract"
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Authors
Khaled Elbassioni, Kazuhisa Makino
arXiv ID
1707.03914
Category
cs.DS: Data Structures & Algorithms
Citations
3
Venue
Scandinavian Workshop on Algorithm Theory
Last Checked
4 months ago
Abstract
We give an incremental polynomial time algorithm for enumerating the vertices of any polyhedron $\mathcal{P}(A,\mathbf{1})=\{x\in\RR^n \mid Ax\geq \b1,~x\geq \b0\}$, 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.
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