Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

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http://hdl.handle.net/10138/27920

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Floréen , P , Kaski , P , Polishchuk , V & Suomela , J 2010 , ' Almost Stable Matchings by Truncating the Gale–Shapley Algorithm ' , Algorithmica , vol. 58 , no. 1 , pp. 102-118 . https://doi.org/10.1007/s00453-009-9353-9

Title: Almost Stable Matchings by Truncating the Gale–Shapley Algorithm
Author: Floréen, Patrik; Kaski, Petteri; Polishchuk, Valentin; Suomela, Jukka
Contributor: University of Helsinki, Adaptive Computing research group / Patrik Floreen
University of Helsinki, Finnish Centre of Excellence in Algorithmic Data Analysis Research (Algodan)
University of Helsinki, Helsinki Institute for Information Technology
University of Helsinki, Helsinki Institute for Information Technology
Date: 2010
Language: eng
Number of pages: 17
Belongs to series: Algorithmica
ISSN: 0178-4617
URI: http://hdl.handle.net/10138/27920
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.
Subject: 111 Mathematics
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