Brief announcement: a note on distributed stable matching
Proceedings of the 28th ACM symposium on Principles of distributed computing
The round complexity of distributed sorting: extended abstract
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Distributed weighted stable marriage problem
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
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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