A Note on Distributed Stable Matching

14 years 1 months ago

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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 unmatched 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 Ω( n/B log n) communication rounds in the worst case, even for graphs of diameter O(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( √ n) blocking pairs. We also consider ε-stability, where a pair is called ε-blocking if they can improve the quality of their

Alex Kipnis, Boaz Patt-Shamir

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