Enumerating Vertices of $0/1$-Polyhedra associated with $0/1$-Totally Unimodular Matrices
Enumerating Vertices of $0/1$-Polyhedra associated with $0/1$-Totally Unimodular Matrices
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.
- Leibniz Association Germany
- Khalifa University of Science and Technology United Arab Emirates
- Schloss Dagstuhl – Leibniz Center for Informatics Germany
FOS: Computer and information sciences, Totally unimodular matrices, Vertex enumeration, 004, 510, Vertices of polyhedra, Hypergraph transversals, Hypergraph decomposition, Output polynomial-time algorithm, Computer Science - Data Structures and Algorithms, Data Structures and Algorithms (cs.DS), ddc: ddc:004
FOS: Computer and information sciences, Totally unimodular matrices, Vertex enumeration, 004, 510, Vertices of polyhedra, Hypergraph transversals, Hypergraph decomposition, Output polynomial-time algorithm, Computer Science - Data Structures and Algorithms, Data Structures and Algorithms (cs.DS), ddc: ddc:004
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