{"title":"Enumerating Vertices of $0/1$-Polyhedra associated with $0/1$-Totally Unimodular Matrices","authors":"Khaled M. Elbassioni, K. Makino","doi":"10.4230/LIPIcs.SWAT.2018.18","DOIUrl":null,"url":null,"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.","PeriodicalId":447445,"journal":{"name":"Scandinavian Workshop on Algorithm Theory","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scandinavian Workshop on Algorithm Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.SWAT.2018.18","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
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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