{"title":"A Note on Distributed Stable Matching","authors":"Alexander Kipnis, B. Patt-Shamir","doi":"10.1109/ICDCS.2009.69","DOIUrl":null,"url":null,"abstract":"We consider the distributed complexity of the stable marriage problem. In this problem, the communication graph is undirected and bipartite, and each node ranks its neighbors. Given a matching of the nodes, a pair of nodes is called blocking if they prefer each other to their assigned match. A matching is called stable if it does not induce any blocking pair. In the distributed model, nodes exchange messages in each round over the communication links, until they find a stable matching. We show that if messages may contain at most B bits each, then any distributed algorithm that solves the stable marriage problem requires Omega(sqrt(n/(B log n))) communication rounds in the worst case, even for graphs of diameter Theta (log n), where n is the number of nodes in the graph. Furthermore, the lower bound holds even if we allow the output to contain O(sqrt(n)) blocking pairs. We also consider epsilon-stability, where a pair is called epsilon-blocking if they can improve the quality of their match by more than an epsilon fraction, for some 0","PeriodicalId":387968,"journal":{"name":"2009 29th IEEE International Conference on Distributed Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2009-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 29th IEEE International Conference on Distributed Computing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICDCS.2009.69","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 12
Abstract
We consider the distributed complexity of the stable marriage problem. In this problem, the communication graph is undirected and bipartite, and each node ranks its neighbors. Given a matching of the nodes, a pair of nodes is called blocking if they prefer each other to their assigned match. A matching is called stable if it does not induce any blocking pair. In the distributed model, nodes exchange messages in each round over the communication links, until they find a stable matching. We show that if messages may contain at most B bits each, then any distributed algorithm that solves the stable marriage problem requires Omega(sqrt(n/(B log n))) communication rounds in the worst case, even for graphs of diameter Theta (log n), where n is the number of nodes in the graph. Furthermore, the lower bound holds even if we allow the output to contain O(sqrt(n)) blocking pairs. We also consider epsilon-stability, where a pair is called epsilon-blocking if they can improve the quality of their match by more than an epsilon fraction, for some 0