A note on distributed stable matching

Alex Kipnis*, Boaz Patt-Shamir

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 Ω(√n/B log 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. 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 match by more than an ε fraction, for some 0 ≤ ε ≤ 1. Our lower bound extends to ε-stability where " is arbitrarily close to 1/2. We also present a simple distributed algorithm for ε-stability whose time complexity is O(n/ε)

Original languageEnglish
Title of host publication2009 29th IEEE International Conference on Distributed Computing Systems Workshops, ICDCS, 09
Pages466-473
Number of pages8
DOIs
StatePublished - 2009
Event2009 29th IEEE International Conference on Distributed Computing Systems Workshops, ICDCS, 09 - Montreal, QC, Canada
Duration: 22 Jun 200926 Jun 2009

Publication series

NameProceedings - International Conference on Distributed Computing Systems

Conference

Conference2009 29th IEEE International Conference on Distributed Computing Systems Workshops, ICDCS, 09
Country/TerritoryCanada
CityMontreal, QC
Period22/06/0926/06/09

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