{"title":"平面网络中最小切割和最大流量的并行算法","authors":"Donald B. Johnson, S. M. Venkatesan","doi":"10.1145/31846.31849","DOIUrl":null,"url":null,"abstract":"Algorithms are given that compute maximum flows in planar directed networks either in O((logn)3) parallel time using O(n4) processors or O((logn)2) parallel time using O(n6) processors. The resource consumption of these algorithms is dominated by the cost of finding the value of a maximum flow. When such a value is given, or when the computation is on an undirected network, the bound is O((logn)2) time using O(n4) processors. No efficient parallel algorithm is known for the maximum flow problem in general networks.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"74 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"51","resultStr":"{\"title\":\"Parallel algorithms for minimum cuts and maximum flows in planar networks\",\"authors\":\"Donald B. Johnson, S. M. Venkatesan\",\"doi\":\"10.1145/31846.31849\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Algorithms are given that compute maximum flows in planar directed networks either in O((logn)3) parallel time using O(n4) processors or O((logn)2) parallel time using O(n6) processors. The resource consumption of these algorithms is dominated by the cost of finding the value of a maximum flow. When such a value is given, or when the computation is on an undirected network, the bound is O((logn)2) time using O(n4) processors. No efficient parallel algorithm is known for the maximum flow problem in general networks.\",\"PeriodicalId\":127919,\"journal\":{\"name\":\"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)\",\"volume\":\"74 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1982-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"51\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/31846.31849\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/31846.31849","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Parallel algorithms for minimum cuts and maximum flows in planar networks
Algorithms are given that compute maximum flows in planar directed networks either in O((logn)3) parallel time using O(n4) processors or O((logn)2) parallel time using O(n6) processors. The resource consumption of these algorithms is dominated by the cost of finding the value of a maximum flow. When such a value is given, or when the computation is on an undirected network, the bound is O((logn)2) time using O(n4) processors. No efficient parallel algorithm is known for the maximum flow problem in general networks.
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