A Stable Marriage Requires Communication
Yannai A. Gonczarowski, Noam Nisan, Rafail Ostrovsky, Will Rosenbaum

TL;DR
This paper proves that finding a stable marriage requires quadratic communication complexity, even approximately, by reducing the problem to the disjointness problem, thus establishing fundamental lower bounds in various models.
Contribution
It introduces a simplified, powerful communication complexity lower bound for stable marriage, extending to randomized algorithms, variants, and approximate stability.
Findings
Quadratic lower bound on Boolean queries for stable marriage
Lower bounds apply to randomized and preprocessing models
Efficient algorithm for computing distance to stability
Abstract
The Gale-Shapley algorithm for the Stable Marriage Problem is known to take steps to find a stable marriage in the worst case, but only steps in the average case (with women and men). In 1976, Knuth asked whether the worst-case running time can be improved in a model of computation that does not require sequential access to the whole input. A partial negative answer was given by Ng and Hirschberg, who showed that queries are required in a model that allows certain natural random-access queries to the participants' preferences. A significantly more general - albeit slightly weaker - lower bound follows from Segal's general analysis of communication complexity, namely that Boolean queries are required in order to find a stable marriage, regardless of the set of allowed Boolean queries. Using a reduction to the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGame Theory and Voting Systems · Logic, Reasoning, and Knowledge · Complexity and Algorithms in Graphs
