A stable marriage requires communication

Yannai A. Gonczarowski, Noam Nisan, Rafail Ostrovsky and Will Rosenbaum

Games and Economic Behavior, 2019, vol. 118, issue C, 626-647

Abstract: In 1976, Knuth asked whether the worst-case running-time of the Gale-Shapley algorithm for the Stable Marriage Problem can be improved when non-sequential access to the input is allowed. Partial negative answers were given by Ng and Hirschberg and as part of Segal's general communication-complexity analysis. We give a far simpler, yet significantly more powerful, argument showing that Ω(n2) Boolean queries of any type are required for finding a stable — or even approximately stable — marriage. Unlike Segal's lower bound, our lower bound generalizes additionally to (A) randomized algorithms, (B) allowing arbitrary separate preprocessing of the women's and men's respective preferences profiles, (C) related problems, e.g. whether a given pair is married in every/some stable marriage, (D) whether a proposed marriage is stable or far from stable. To analyze “approximately stable” marriages, we introduce the notion of “distance to stability” and provide an efficient algorithm for its computation.

Keywords: Stable marriage; Stable matching; Approximately stable; Communication complexity; Distance to stability (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Working Paper: A Stable Marriage Requires Communication (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:118:y:2019:i:c:p:626-647

DOI: 10.1016/j.geb.2018.10.013

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