{"title":"分布式通信协议中分配问题的渐近分析","authors":"B. Hajek","doi":"10.1109/CDC.1988.194566","DOIUrl":null,"url":null,"abstract":"Matchings for a random bipartite graph are considered. Each of the alpha M nodes on one side of the graph is directly connected to Q nodes chosen randomly and uniformly from among the M nodes on the other side of the graph. The size matchings found by two simple approximation algorithms, as well as the size of the maximum matching when Q=2, are asymptotically determined in the limit as Q tends to infinity with alpha fixed. The work is motivated by a distributed communications protocol for accessing a silent receiver. The theory of approximating slow Markov random walks by ordinary differential equations is used for the analysis.<<ETX>>","PeriodicalId":113534,"journal":{"name":"Proceedings of the 27th IEEE Conference on Decision and Control","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Asymptotic analysis of an assignment problem arising in a distributed communications protocol\",\"authors\":\"B. Hajek\",\"doi\":\"10.1109/CDC.1988.194566\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Matchings for a random bipartite graph are considered. Each of the alpha M nodes on one side of the graph is directly connected to Q nodes chosen randomly and uniformly from among the M nodes on the other side of the graph. The size matchings found by two simple approximation algorithms, as well as the size of the maximum matching when Q=2, are asymptotically determined in the limit as Q tends to infinity with alpha fixed. The work is motivated by a distributed communications protocol for accessing a silent receiver. The theory of approximating slow Markov random walks by ordinary differential equations is used for the analysis.<<ETX>>\",\"PeriodicalId\":113534,\"journal\":{\"name\":\"Proceedings of the 27th IEEE Conference on Decision and Control\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 27th IEEE Conference on Decision and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1988.194566\",\"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 27th IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1988.194566","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Asymptotic analysis of an assignment problem arising in a distributed communications protocol
Matchings for a random bipartite graph are considered. Each of the alpha M nodes on one side of the graph is directly connected to Q nodes chosen randomly and uniformly from among the M nodes on the other side of the graph. The size matchings found by two simple approximation algorithms, as well as the size of the maximum matching when Q=2, are asymptotically determined in the limit as Q tends to infinity with alpha fixed. The work is motivated by a distributed communications protocol for accessing a silent receiver. The theory of approximating slow Markov random walks by ordinary differential equations is used for the analysis.<>
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