{"title":"分布式图算法从本地数据的全局解决方案","authors":"N. Linial","doi":"10.1109/SFCS.1987.20","DOIUrl":null,"url":null,"abstract":"This paper deals with distributed graph algorithms. Processors reside in the vertices of a graph G and communicate only with their neighbors. The system is synchronous and reliable, there is no limit on message lengths and local computation is instantaneous. The results: A maximal independent set in an n-cycle cannot be found faster than Ω(log* n) and this is optimal by [CV]. The d-regular tree of radius r cannot be colored with fewer than √d colors in time 2r / 3. If Δ is the largest degree in G which has order n, then in time O(log*n) it can be colored with O(Δ2) colors.","PeriodicalId":153779,"journal":{"name":"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1987-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"209","resultStr":"{\"title\":\"Distributive graph algorithms Global solutions from local data\",\"authors\":\"N. Linial\",\"doi\":\"10.1109/SFCS.1987.20\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with distributed graph algorithms. Processors reside in the vertices of a graph G and communicate only with their neighbors. The system is synchronous and reliable, there is no limit on message lengths and local computation is instantaneous. The results: A maximal independent set in an n-cycle cannot be found faster than Ω(log* n) and this is optimal by [CV]. The d-regular tree of radius r cannot be colored with fewer than √d colors in time 2r / 3. If Δ is the largest degree in G which has order n, then in time O(log*n) it can be colored with O(Δ2) colors.\",\"PeriodicalId\":153779,\"journal\":{\"name\":\"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1987-10-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"209\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1987.20\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1987.20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Distributive graph algorithms Global solutions from local data
This paper deals with distributed graph algorithms. Processors reside in the vertices of a graph G and communicate only with their neighbors. The system is synchronous and reliable, there is no limit on message lengths and local computation is instantaneous. The results: A maximal independent set in an n-cycle cannot be found faster than Ω(log* n) and this is optimal by [CV]. The d-regular tree of radius r cannot be colored with fewer than √d colors in time 2r / 3. If Δ is the largest degree in G which has order n, then in time O(log*n) it can be colored with O(Δ2) colors.