{"title":"基于0-1二次优化的稳定集和着色界","authors":"Dunja Pucher, F. Rendl","doi":"10.23952/asvao.5.2023.2.08","DOIUrl":null,"url":null,"abstract":"We consider semidefinite relaxations of Stable-Set and Coloring, which are based on quadratic 0-1 optimization. Information about the stability number and the chromatic number is hidden in the objective function. This leads to simplified relaxations which depend mostly on the number of vertices of the graph. We also propose tightenings of the relaxations which are based on the maximal cliques of the underlying graph. Computational results on graphs from the literature show the strong potential of this new approach.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"19 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stable-set and coloring bounds based on 0-1 quadratic optimization\",\"authors\":\"Dunja Pucher, F. Rendl\",\"doi\":\"10.23952/asvao.5.2023.2.08\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider semidefinite relaxations of Stable-Set and Coloring, which are based on quadratic 0-1 optimization. Information about the stability number and the chromatic number is hidden in the objective function. This leads to simplified relaxations which depend mostly on the number of vertices of the graph. We also propose tightenings of the relaxations which are based on the maximal cliques of the underlying graph. Computational results on graphs from the literature show the strong potential of this new approach.\",\"PeriodicalId\":362333,\"journal\":{\"name\":\"Applied Set-Valued Analysis and Optimization\",\"volume\":\"19 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Set-Valued Analysis and Optimization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23952/asvao.5.2023.2.08\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Set-Valued Analysis and Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/asvao.5.2023.2.08","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stable-set and coloring bounds based on 0-1 quadratic optimization
We consider semidefinite relaxations of Stable-Set and Coloring, which are based on quadratic 0-1 optimization. Information about the stability number and the chromatic number is hidden in the objective function. This leads to simplified relaxations which depend mostly on the number of vertices of the graph. We also propose tightenings of the relaxations which are based on the maximal cliques of the underlying graph. Computational results on graphs from the literature show the strong potential of this new approach.
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