{"title":"规划快速连接更新","authors":"M. Patrascu, Mikkel Thorup","doi":"10.1109/FOCS.2007.54","DOIUrl":null,"url":null,"abstract":"Understanding how a single edge deletion can affect the connectivity of a graph amounts to finding the graph bridges. But when faced with d. > l deletions, can we establish as easily how the connectivity changes? When planning for an emergency, we want to understand the structure of our network ahead of time, and respond swiftly when an emergency actually happens. We describe a linear-space representation of graphs which enables us to determine how a batch of edge updates can impact the graph. Given a set of d edge updates, in time O(d polylg n) we can obtain the number of connected components, the size of each component, and a fast oracle for answering connectivity queries in the updated graph. The initial representation is polynomial-time constructible.","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"80","resultStr":"{\"title\":\"Planning for Fast Connectivity Updates\",\"authors\":\"M. Patrascu, Mikkel Thorup\",\"doi\":\"10.1109/FOCS.2007.54\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Understanding how a single edge deletion can affect the connectivity of a graph amounts to finding the graph bridges. But when faced with d. > l deletions, can we establish as easily how the connectivity changes? When planning for an emergency, we want to understand the structure of our network ahead of time, and respond swiftly when an emergency actually happens. We describe a linear-space representation of graphs which enables us to determine how a batch of edge updates can impact the graph. Given a set of d edge updates, in time O(d polylg n) we can obtain the number of connected components, the size of each component, and a fast oracle for answering connectivity queries in the updated graph. The initial representation is polynomial-time constructible.\",\"PeriodicalId\":197431,\"journal\":{\"name\":\"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-10-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"80\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FOCS.2007.54\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FOCS.2007.54","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Understanding how a single edge deletion can affect the connectivity of a graph amounts to finding the graph bridges. But when faced with d. > l deletions, can we establish as easily how the connectivity changes? When planning for an emergency, we want to understand the structure of our network ahead of time, and respond swiftly when an emergency actually happens. We describe a linear-space representation of graphs which enables us to determine how a batch of edge updates can impact the graph. Given a set of d edge updates, in time O(d polylg n) we can obtain the number of connected components, the size of each component, and a fast oracle for answering connectivity queries in the updated graph. The initial representation is polynomial-time constructible.
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