{"title":"枚举$0/1$的顶点-与$0/1$相关的多面体-完全非模矩阵","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":"{\"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}","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}
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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