Brief announcement: 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

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/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. 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).

Original languageEnglish
Title of host publicationPODC'09 - Proceedings of the 2009 ACM Symposium on Principles of Distributed Computing
Pages282-283
Number of pages2
DOIs
StatePublished - 2009
Event2009 ACM Symposium on Principles of Distributed Computing, PODC'09 - Calgary, AB, Canada
Duration: 10 Aug 200912 Aug 2009

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference2009 ACM Symposium on Principles of Distributed Computing, PODC'09
Country/TerritoryCanada
CityCalgary, AB
Period10/08/0912/08/09

Keywords

  • Communication complexity
  • Game theory
  • Stable marriage

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