{"title":"最小生成树多边更新的并行算法","authors":"Xiaojun Shen, W. Liang","doi":"10.1109/IPPS.1993.262898","DOIUrl":null,"url":null,"abstract":"The authors present a parallel algorithm for the multiple edge update problem on a minimum spanning tree. This problem is defined as follows: given a minimum spanning tree T(V,E/sub T/) of an undirected graph G(V,E), where mod V mod =n and E/sub T/ is the set of tree edges, recompute a new minimum spanning tree when (1) adding K new edges, (2) changing the weights of existent K edges, or (3) deleting a vertex of degree K in the tree, where 1<or=K<n. Their algorithm requires O(logKlogn) time and O(n/sup 2//lognlogK) processors on a SIMD CREW PRAM model. If the weights of the current tree edges are not allowed to increase, then their algorithm runs in the same time bound, but only using O(max(n,nK/lognlogK)) processors. Their algorithm is optimal for dense graphs, if no intermediate results are available from computing the original MST.<<ETX>>","PeriodicalId":248927,"journal":{"name":"[1993] Proceedings Seventh International Parallel Processing Symposium","volume":"18 3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"A parallel algorithm for multiple edge updates of minimum spanning trees\",\"authors\":\"Xiaojun Shen, W. Liang\",\"doi\":\"10.1109/IPPS.1993.262898\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The authors present a parallel algorithm for the multiple edge update problem on a minimum spanning tree. This problem is defined as follows: given a minimum spanning tree T(V,E/sub T/) of an undirected graph G(V,E), where mod V mod =n and E/sub T/ is the set of tree edges, recompute a new minimum spanning tree when (1) adding K new edges, (2) changing the weights of existent K edges, or (3) deleting a vertex of degree K in the tree, where 1<or=K<n. Their algorithm requires O(logKlogn) time and O(n/sup 2//lognlogK) processors on a SIMD CREW PRAM model. If the weights of the current tree edges are not allowed to increase, then their algorithm runs in the same time bound, but only using O(max(n,nK/lognlogK)) processors. Their algorithm is optimal for dense graphs, if no intermediate results are available from computing the original MST.<<ETX>>\",\"PeriodicalId\":248927,\"journal\":{\"name\":\"[1993] Proceedings Seventh International Parallel Processing Symposium\",\"volume\":\"18 3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-04-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1993] Proceedings Seventh International Parallel Processing Symposium\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IPPS.1993.262898\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1993] Proceedings Seventh International Parallel Processing Symposium","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IPPS.1993.262898","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 14
摘要
提出了一种求解最小生成树多边更新问题的并行算法。该问题定义如下:给定无向图G(V,E)的最小生成树T(V,E/下标T/),其中mod V mod =n,E/下标T/为树边的集合,当(1)添加K条新边,(2)改变现有K条边的权值,或(3)删除树中K度的顶点,其中1>
A parallel algorithm for multiple edge updates of minimum spanning trees
The authors present a parallel algorithm for the multiple edge update problem on a minimum spanning tree. This problem is defined as follows: given a minimum spanning tree T(V,E/sub T/) of an undirected graph G(V,E), where mod V mod =n and E/sub T/ is the set of tree edges, recompute a new minimum spanning tree when (1) adding K new edges, (2) changing the weights of existent K edges, or (3) deleting a vertex of degree K in the tree, where 1>