{"title":"展开图中的弧不相交路径","authors":"T. Bohman, A. Frieze","doi":"10.1109/SFCS.2001.959932","DOIUrl":null,"url":null,"abstract":"Given a digraph D=(V, A) and a set of /spl kappa/ pairs of vertices in V, we are interested in finding for each pair (x/sub i/, y/sub i/), a directed path connecting x/sub i/ to y/sub i/, such that the set of /spl kappa/ paths so found is arc-disjoint. For arbitrary graphs, the problem is /spl Nscr//spl Pscr/-complete, even for /spl kappa/=2. We present a polynomial time randomized algorithm for finding arc-disjoint paths in an r-regular expander digraph D. We show that if D has sufficiently strong expansion properties and r is sufficiently large, then all sets of /spl kappa/=/spl Omega/(n/log n) pairs of vertices can be joined. This is within a constant factor of best possible.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Arc-disjoint paths in expander digraphs\",\"authors\":\"T. Bohman, A. Frieze\",\"doi\":\"10.1109/SFCS.2001.959932\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a digraph D=(V, A) and a set of /spl kappa/ pairs of vertices in V, we are interested in finding for each pair (x/sub i/, y/sub i/), a directed path connecting x/sub i/ to y/sub i/, such that the set of /spl kappa/ paths so found is arc-disjoint. For arbitrary graphs, the problem is /spl Nscr//spl Pscr/-complete, even for /spl kappa/=2. We present a polynomial time randomized algorithm for finding arc-disjoint paths in an r-regular expander digraph D. We show that if D has sufficiently strong expansion properties and r is sufficiently large, then all sets of /spl kappa/=/spl Omega/(n/log n) pairs of vertices can be joined. This is within a constant factor of best possible.\",\"PeriodicalId\":378126,\"journal\":{\"name\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"volume\":\"43 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.2001.959932\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 2001 IEEE International Conference on Cluster Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.2001.959932","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Given a digraph D=(V, A) and a set of /spl kappa/ pairs of vertices in V, we are interested in finding for each pair (x/sub i/, y/sub i/), a directed path connecting x/sub i/ to y/sub i/, such that the set of /spl kappa/ paths so found is arc-disjoint. For arbitrary graphs, the problem is /spl Nscr//spl Pscr/-complete, even for /spl kappa/=2. We present a polynomial time randomized algorithm for finding arc-disjoint paths in an r-regular expander digraph D. We show that if D has sufficiently strong expansion properties and r is sufficiently large, then all sets of /spl kappa/=/spl Omega/(n/log n) pairs of vertices can be joined. This is within a constant factor of best possible.
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