{"title":"偏置表示在边连通性和图刚性中的应用","authors":"H. Gabow","doi":"10.1109/SFCS.1991.185453","DOIUrl":null,"url":null,"abstract":"A poset representation for a family of sets defined by a labeling algorithm is investigated. Poset representations are given for the family of minimum cuts of a graph, and it is shown how to compute them quickly. The representations are the starting point for algorithms that increase the edge connectivity of a graph, from lambda to a given target tau = lambda + delta , adding the fewest edges possible. For undirected graphs the time bound is essentially the best-known bound to test tau -edge connectivity; for directed graphs the time bound is roughly a factor delta more. Also constructed are poset representations for the family of rigid subgraphs of a graph, when graphs model structures constructed from rigid bars. The link between these problems is that they all deal with graphic matroids.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"34 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"101","resultStr":"{\"title\":\"Applications of a poset representation to edge connectivity and graph rigidity\",\"authors\":\"H. Gabow\",\"doi\":\"10.1109/SFCS.1991.185453\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A poset representation for a family of sets defined by a labeling algorithm is investigated. Poset representations are given for the family of minimum cuts of a graph, and it is shown how to compute them quickly. The representations are the starting point for algorithms that increase the edge connectivity of a graph, from lambda to a given target tau = lambda + delta , adding the fewest edges possible. For undirected graphs the time bound is essentially the best-known bound to test tau -edge connectivity; for directed graphs the time bound is roughly a factor delta more. Also constructed are poset representations for the family of rigid subgraphs of a graph, when graphs model structures constructed from rigid bars. The link between these problems is that they all deal with graphic matroids.<<ETX>>\",\"PeriodicalId\":320781,\"journal\":{\"name\":\"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science\",\"volume\":\"34 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"101\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1991.185453\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1991.185453","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Applications of a poset representation to edge connectivity and graph rigidity
A poset representation for a family of sets defined by a labeling algorithm is investigated. Poset representations are given for the family of minimum cuts of a graph, and it is shown how to compute them quickly. The representations are the starting point for algorithms that increase the edge connectivity of a graph, from lambda to a given target tau = lambda + delta , adding the fewest edges possible. For undirected graphs the time bound is essentially the best-known bound to test tau -edge connectivity; for directed graphs the time bound is roughly a factor delta more. Also constructed are poset representations for the family of rigid subgraphs of a graph, when graphs model structures constructed from rigid bars. The link between these problems is that they all deal with graphic matroids.<>