{"title":"全局基数约束的复杂性","authors":"A. Bulatov, D. Marx","doi":"10.2168/LMCS-6(4:4)2010","DOIUrl":null,"url":null,"abstract":"In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must be assigned a certain value. We study the complexity of the problem CCSP(Gamma), the constraint satisfaction problem with global cardinality constraints that allows only relations from the set Gamma. The main result of this paper characterizes sets Gamma that give rise to problems solvable in polynomial time, and states that the remaining such problems are NP-complete.","PeriodicalId":415902,"journal":{"name":"2009 24th Annual IEEE Symposium on Logic In Computer Science","volume":"41 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":"{\"title\":\"The Complexity of Global Cardinality Constraints\",\"authors\":\"A. Bulatov, D. Marx\",\"doi\":\"10.2168/LMCS-6(4:4)2010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must be assigned a certain value. We study the complexity of the problem CCSP(Gamma), the constraint satisfaction problem with global cardinality constraints that allows only relations from the set Gamma. The main result of this paper characterizes sets Gamma that give rise to problems solvable in polynomial time, and states that the remaining such problems are NP-complete.\",\"PeriodicalId\":415902,\"journal\":{\"name\":\"2009 24th Annual IEEE Symposium on Logic In Computer Science\",\"volume\":\"41 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-08-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"21\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 24th Annual IEEE Symposium on Logic In Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2168/LMCS-6(4:4)2010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 24th Annual IEEE Symposium on Logic In Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2168/LMCS-6(4:4)2010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must be assigned a certain value. We study the complexity of the problem CCSP(Gamma), the constraint satisfaction problem with global cardinality constraints that allows only relations from the set Gamma. The main result of this paper characterizes sets Gamma that give rise to problems solvable in polynomial time, and states that the remaining such problems are NP-complete.
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