Algorithmica

, Volume 58, Issue 1, pp 102–118 | Cite as

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

  • Patrik Floréen
  • Petteri Kaski
  • Valentin Polishchuk
  • Jukka Suomela
Article

Abstract

We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds.

We apply our results to give a distributed (2+ε)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching.

Keywords

Distributed stable matching Almost stable matching Local algorithms Constant-time randomised algorithms 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Patrik Floréen
    • 1
  • Petteri Kaski
    • 1
  • Valentin Polishchuk
    • 1
  • Jukka Suomela
    • 1
  1. 1.Helsinki Institute for Information Technology HIITUniversity of HelsinkiHelsinkiFinland

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