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arXiv · 2405.01039

A first efficient algorithm for enumerating all the extreme points of a bisubmodular polyhedron

Yasuko Matsui·Takeshi Naitoh·Ping Zhan
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Abstract

Efficiently enumerating all the extreme points of a polytope identified by a system of linear inequalities is a well-known challenge issue.We consider a special case and present an algorithm that enumerates all the extreme points of a bisubmodular polyhedron in $\mathcal{O}(n^4|V|)$ time and $\mathcal{O}(n^2)$ space complexity, where $ n$ is the dimension of underlying space and $V$ is the set of outputs. We use the reverse search and signed poset linked to extreme points to avoid the redundant search. Our algorithm is a generalization of enumerating all the extreme points of a base polyhedron which comprises some combinatorial enumeration problems.

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Yasuko Matsui, Takeshi Naitoh, Ping Zhan. 2024-05-02. A first efficient algorithm for enumerating all the extreme points of a bisubmodular polyhedron. https://arxiv.org/abs/2405.01039

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