{"title":"随机二部最近邻图","authors":"B. Pittel, Robert S. Weishaar","doi":"10.1002/(SICI)1098-2418(199910/12)15:3/4%3C279::AID-RSA6%3E3.0.CO;2-J","DOIUrl":null,"url":null,"abstract":"The bipartite kth nearest neighbor graphs B are studied. It is shown that B k 1 has a limiting expected matching number of approximately 80% of its vertices, that with high Ž . probability whp B has at least 2 log nr13 log log n vertices not matched, and that whp B 2 3 does have a perfect matching. We also find a formula for the limiting probability that B is 2 connected and show that whp B is connected. Q 1999 John Wiley & Sons, Inc. Random Struct. 3 Alg., 15, 279]310, 1999","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"18 9-10","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"The random bipartite nearest neighbor graphs\",\"authors\":\"B. Pittel, Robert S. Weishaar\",\"doi\":\"10.1002/(SICI)1098-2418(199910/12)15:3/4%3C279::AID-RSA6%3E3.0.CO;2-J\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The bipartite kth nearest neighbor graphs B are studied. It is shown that B k 1 has a limiting expected matching number of approximately 80% of its vertices, that with high Ž . probability whp B has at least 2 log nr13 log log n vertices not matched, and that whp B 2 3 does have a perfect matching. We also find a formula for the limiting probability that B is 2 connected and show that whp B is connected. Q 1999 John Wiley & Sons, Inc. Random Struct. 3 Alg., 15, 279]310, 1999\",\"PeriodicalId\":303496,\"journal\":{\"name\":\"Random Struct. Algorithms\",\"volume\":\"18 9-10\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Struct. Algorithms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/(SICI)1098-2418(199910/12)15:3/4%3C279::AID-RSA6%3E3.0.CO;2-J\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/(SICI)1098-2418(199910/12)15:3/4%3C279::AID-RSA6%3E3.0.CO;2-J","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The bipartite kth nearest neighbor graphs B are studied. It is shown that B k 1 has a limiting expected matching number of approximately 80% of its vertices, that with high Ž . probability whp B has at least 2 log nr13 log log n vertices not matched, and that whp B 2 3 does have a perfect matching. We also find a formula for the limiting probability that B is 2 connected and show that whp B is connected. Q 1999 John Wiley & Sons, Inc. Random Struct. 3 Alg., 15, 279]310, 1999
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