{"title":"完全图中的精确完美匹配","authors":"R. Gurjar, A. Korwar, J. Messner, T. Thierauf","doi":"10.1145/3041402","DOIUrl":null,"url":null,"abstract":"A red-blue graph is a graph where every edge is colored either red or blue. The exact perfect matching problem asks for a perfect matching in a red-blue graph that has exactly a given number of red edges. We show that for complete and bipartite complete graphs, the exact perfect matching problem is logspace equivalent to the perfect matching problem. Hence, an efficient parallel algorithm for perfect matching would carry over to the exact perfect matching problem for this class of graphs. We also report some progress in extending the result to arbitrary graphs.","PeriodicalId":198744,"journal":{"name":"ACM Transactions on Computation Theory (TOCT)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Exact Perfect Matching in Complete Graphs\",\"authors\":\"R. Gurjar, A. Korwar, J. Messner, T. Thierauf\",\"doi\":\"10.1145/3041402\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A red-blue graph is a graph where every edge is colored either red or blue. The exact perfect matching problem asks for a perfect matching in a red-blue graph that has exactly a given number of red edges. We show that for complete and bipartite complete graphs, the exact perfect matching problem is logspace equivalent to the perfect matching problem. Hence, an efficient parallel algorithm for perfect matching would carry over to the exact perfect matching problem for this class of graphs. We also report some progress in extending the result to arbitrary graphs.\",\"PeriodicalId\":198744,\"journal\":{\"name\":\"ACM Transactions on Computation Theory (TOCT)\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-04-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Transactions on Computation Theory (TOCT)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3041402\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Computation Theory (TOCT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3041402","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A red-blue graph is a graph where every edge is colored either red or blue. The exact perfect matching problem asks for a perfect matching in a red-blue graph that has exactly a given number of red edges. We show that for complete and bipartite complete graphs, the exact perfect matching problem is logspace equivalent to the perfect matching problem. Hence, an efficient parallel algorithm for perfect matching would carry over to the exact perfect matching problem for this class of graphs. We also report some progress in extending the result to arbitrary graphs.
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