{"title":"非均匀稳定匹配","authors":"Naoyuki Kamiyama","doi":"arxiv-2408.16271","DOIUrl":null,"url":null,"abstract":"Super-stability and strong stability are properties of a matching in the\nstable matching problem with ties. In this paper, we introduce a common\ngeneralization of super-stability and strong stability, which we call\nnon-uniform stability. First, we prove that we can determine the existence of a\nnon-uniformly stable matching in polynomial time. Next, we give a polyhedral\ncharacterization of the set of non-uniformly stable matchings. Finally, we\nprove that the set of non-uniformly stable matchings forms a distributive\nlattice.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"63 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-uniformly Stable Matchings\",\"authors\":\"Naoyuki Kamiyama\",\"doi\":\"arxiv-2408.16271\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Super-stability and strong stability are properties of a matching in the\\nstable matching problem with ties. In this paper, we introduce a common\\ngeneralization of super-stability and strong stability, which we call\\nnon-uniform stability. First, we prove that we can determine the existence of a\\nnon-uniformly stable matching in polynomial time. Next, we give a polyhedral\\ncharacterization of the set of non-uniformly stable matchings. Finally, we\\nprove that the set of non-uniformly stable matchings forms a distributive\\nlattice.\",\"PeriodicalId\":501316,\"journal\":{\"name\":\"arXiv - CS - Computer Science and Game Theory\",\"volume\":\"63 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Computer Science and Game Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.16271\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computer Science and Game Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.16271","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Super-stability and strong stability are properties of a matching in the
stable matching problem with ties. In this paper, we introduce a common
generalization of super-stability and strong stability, which we call
non-uniform stability. First, we prove that we can determine the existence of a
non-uniformly stable matching in polynomial time. Next, we give a polyhedral
characterization of the set of non-uniformly stable matchings. Finally, we
prove that the set of non-uniformly stable matchings forms a distributive
lattice.
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