{"title":"具有实边权的全动态全对最短路径","authors":"C. Demetrescu, G. Italiano","doi":"10.1109/SFCS.2001.959900","DOIUrl":null,"url":null,"abstract":"We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. Given a dynamic directed graph G such that each edge can assume at most S different real values, we show how to support updates deterministically in O(S/spl middot/n/sup 2.5/log/sup 3/n) amortized time and queries in optimal worst-case time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with one-sided error which supports updates faster in O(S/spl middot/nlog/sup 3/n) amortized time.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"141 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"118","resultStr":"{\"title\":\"Fully dynamic all pairs shortest paths with real edge weights\",\"authors\":\"C. Demetrescu, G. Italiano\",\"doi\":\"10.1109/SFCS.2001.959900\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. Given a dynamic directed graph G such that each edge can assume at most S different real values, we show how to support updates deterministically in O(S/spl middot/n/sup 2.5/log/sup 3/n) amortized time and queries in optimal worst-case time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with one-sided error which supports updates faster in O(S/spl middot/nlog/sup 3/n) amortized time.\",\"PeriodicalId\":378126,\"journal\":{\"name\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"volume\":\"141 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"118\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.2001.959900\",\"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.2001.959900","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fully dynamic all pairs shortest paths with real edge weights
We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. Given a dynamic directed graph G such that each edge can assume at most S different real values, we show how to support updates deterministically in O(S/spl middot/n/sup 2.5/log/sup 3/n) amortized time and queries in optimal worst-case time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with one-sided error which supports updates faster in O(S/spl middot/nlog/sup 3/n) amortized time.
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