A first efficient algorithm for enumerating all the extreme points of a bisubmodular polyhedron
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917711200649216 |
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| author | Matsui, Yasuko Naitoh, Takeshi Zhan, Ping |
| author_facet | Matsui, Yasuko Naitoh, Takeshi Zhan, Ping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01039 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A first efficient algorithm for enumerating all the extreme points of a bisubmodular polyhedron Matsui, Yasuko Naitoh, Takeshi Zhan, Ping Discrete Mathematics G.2.1 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. |
| title | A first efficient algorithm for enumerating all the extreme points of a bisubmodular polyhedron |
| topic | Discrete Mathematics G.2.1 |
| url | https://arxiv.org/abs/2405.01039 |