Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

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 t...

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Veröffentlicht in:Algorithmica Jg. 58; H. 1; S. 102 - 118
Hauptverfasser: Floréen, Patrik, Kaski, Petteri, Polishchuk, Valentin, Suomela, Jukka
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer-Verlag 01.09.2010
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Mathematics of Computing
Theory of Computation
Distributed stable matching
Local algorithms
Constant-time randomised algorithms
Almost stable matching
ISSN:0178-4617, 1432-0541
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Zusammenfassung: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.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-009-9353-9