{"title":"稀疏图中独立集的计数","authors":"M. Dyer, A. Frieze, M. Jerrum","doi":"10.1109/SFFCS.1999.814593","DOIUrl":null,"url":null,"abstract":"We prove two results concerning approximate counting of independent sets in graphs with constant maximum degree /spl Delta/. The first result implies that the Monte-Carlo Markov chain technique is likely to fail if /spl Delta//spl ges/6. The second shows that no fully polynomial randomized approximation scheme can exist for /spl Delta//spl ges/25, unless P=NP under randomized reductions.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"182","resultStr":"{\"title\":\"On counting independent sets in sparse graphs\",\"authors\":\"M. Dyer, A. Frieze, M. Jerrum\",\"doi\":\"10.1109/SFFCS.1999.814593\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove two results concerning approximate counting of independent sets in graphs with constant maximum degree /spl Delta/. The first result implies that the Monte-Carlo Markov chain technique is likely to fail if /spl Delta//spl ges/6. The second shows that no fully polynomial randomized approximation scheme can exist for /spl Delta//spl ges/25, unless P=NP under randomized reductions.\",\"PeriodicalId\":385047,\"journal\":{\"name\":\"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)\",\"volume\":\"39 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"182\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFFCS.1999.814593\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFFCS.1999.814593","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove two results concerning approximate counting of independent sets in graphs with constant maximum degree /spl Delta/. The first result implies that the Monte-Carlo Markov chain technique is likely to fail if /spl Delta//spl ges/6. The second shows that no fully polynomial randomized approximation scheme can exist for /spl Delta//spl ges/25, unless P=NP under randomized reductions.
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