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Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

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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.

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Authors and Affiliations

  1. Helsinki Institute for Information Technology HIIT, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

    Patrik Floréen, Petteri Kaski, Valentin Polishchuk & Jukka Suomela

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  1. Patrik Floréen
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  2. Petteri Kaski
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  3. Valentin Polishchuk
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  4. Jukka Suomela
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Correspondence to Valentin Polishchuk.

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Floréen, P., Kaski, P., Polishchuk, V. et al. Almost Stable Matchings by Truncating the Gale–Shapley Algorithm. Algorithmica 58, 102–118 (2010). https://doi.org/10.1007/s00453-009-9353-9

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  • DOI: https://doi.org/10.1007/s00453-009-9353-9

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