{"title":"Planar graphs, negative weight edges, shortest paths, and near linear time","authors":"Jittat Fakcharoenphol, Satish Rao","doi":"10.1109/SFCS.2001.959897","DOIUrl":null,"url":null,"abstract":"The authors present an O(n log/sup 3/ n) time algorithm for finding shortest paths in a planar graph with real weights. This can be compared to the best previous strongly polynomial time algorithm developed by R. Lipton et al., (1978 )which ran in O(n/sup 3/2/) time, and the best polynomial algorithm developed by M. Henzinger et al. (1994) which ran in O/spl tilde/(n/sup 4/3/) time. We also present significantly improved algorithms for query and dynamic versions of the shortest path problems.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"253","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 2001 IEEE International Conference on Cluster Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.2001.959897","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 253
Abstract
The authors present an O(n log/sup 3/ n) time algorithm for finding shortest paths in a planar graph with real weights. This can be compared to the best previous strongly polynomial time algorithm developed by R. Lipton et al., (1978 )which ran in O(n/sup 3/2/) time, and the best polynomial algorithm developed by M. Henzinger et al. (1994) which ran in O/spl tilde/(n/sup 4/3/) time. We also present significantly improved algorithms for query and dynamic versions of the shortest path problems.