枚举$0/1$的顶点-与$0/1$相关的多面体-完全非模矩阵

Scandinavian Workshop on Algorithm Theory Pub Date : 2017-07-12 DOI:10.4230/LIPIcs.SWAT.2018.18

Khaled M. Elbassioni, K. Makino

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引用次数: 3

摘要

当$A$是一个完全非模矩阵时，我们给出了枚举任意多面体$\mathcal{P}(A,\mathbf{1})=\{x\in\RR^n \mid Ax\geq \b1,~x\geq \b0\}$顶点的增量多项式时间算法。我们的算法是基于用Seymour的全非模矩阵分解来分解非模超图的截线问题，并且可能具有独立的兴趣。

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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.

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Scandinavian Workshop on Algorithm Theory

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