{"title":"关于逼近极小化问题的硬度","authors":"C. Lund, M. Yannakakis","doi":"10.1145/167088.167172","DOIUrl":null,"url":null,"abstract":"We prove results indicating that it is hard to compute efficiently good approximate solutions to the Graph Coloring, Set Covering and other related minimization problems. Specifically, there is an c >0 such that Graph Coloring cannot be approximated with ratio n’ unless P=NP. Set Covering cannot be approximated with ratio clog n for any c < 1/4 unless NP is contained in DTIME[nPOIY log ~ ]. Similar results follow for related problems such as Clique Cover, Fractional Chromatic Number, Dominating Set and others.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"228","resultStr":"{\"title\":\"On the hardness of approximating minimization problems\",\"authors\":\"C. Lund, M. Yannakakis\",\"doi\":\"10.1145/167088.167172\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove results indicating that it is hard to compute efficiently good approximate solutions to the Graph Coloring, Set Covering and other related minimization problems. Specifically, there is an c >0 such that Graph Coloring cannot be approximated with ratio n’ unless P=NP. Set Covering cannot be approximated with ratio clog n for any c < 1/4 unless NP is contained in DTIME[nPOIY log ~ ]. Similar results follow for related problems such as Clique Cover, Fractional Chromatic Number, Dominating Set and others.\",\"PeriodicalId\":280602,\"journal\":{\"name\":\"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"228\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/167088.167172\",\"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 of the twenty-fifth annual ACM symposium on Theory of Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/167088.167172","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the hardness of approximating minimization problems
We prove results indicating that it is hard to compute efficiently good approximate solutions to the Graph Coloring, Set Covering and other related minimization problems. Specifically, there is an c >0 such that Graph Coloring cannot be approximated with ratio n’ unless P=NP. Set Covering cannot be approximated with ratio clog n for any c < 1/4 unless NP is contained in DTIME[nPOIY log ~ ]. Similar results follow for related problems such as Clique Cover, Fractional Chromatic Number, Dominating Set and others.
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