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arXiv · 0812.4893

Almost stable matchings in constant time

Patrik Floréen·Petteri Kaski·Valentin Polishchuk·Jukka Suomela
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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. This holds even if ties are present in the preference lists. 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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Patrik Floréen, Petteri Kaski, Valentin Polishchuk, Jukka Suomela. 2008-12-29. Almost stable matchings in constant time. https://doi.org/10.1007/s00453-009-9353-9

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