The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
SIAM Journal on Computing
Inapproximability Results on Stable Marriage Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Improved distributed approximate matching
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
A Note on Distributed Stable Matching
ICDCS '09 Proceedings of the 2009 29th IEEE International Conference on Distributed Computing Systems
Matching output queueing with a combined input/output-queued switch
IEEE Journal on Selected Areas in Communications
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In the stable marriage 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 Ω(√n/Blog n) communication rounds in the worst case, even for graphs of diameter Θ(log n), where n is the number of nodes in the graph. The lower bound holds even if the output may 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 match by more than an ε fraction, for some 0 ≤ ε ≤ 1. Our lower bound extends to ε-stability where ε is arbitrarily close to 1/2. We also present a simple distributed algorithm for ε-stability whose time complexity is O(n/ε).