Brief Announcement: Time Efficient Self-stabilizing Stable Marriage

Abstract

“Stable marriage” refers to a particular matching with constraints having a wide variety of applications in different domains (two-sided markets, Cloud computing, college admissions, etc.). Most of the studies on this problem performed up to now were for centralized and synchronous settings assuming initialization. We consider a distributed and asynchronous context, without initialization (i.e., in a self-stabilizing manner, tolerating any transient fault) and with some confidentiality requirements. The single already known self-stabilizing solution in Laveau et al. (SSS’ 2017), based on Ackerman et al.’s algorithm (SICOMP’ 2011), stabilizes in $O(n^4)$ moves (activation of a single node). We improve on this previous result considerably by presenting a solution with $O(n^2)$ steps, relying on the idea of Gale and Shapley’s algorithm (AMM 1962), which takes also $O(n^2)$ moves, but in a centralized synchronous context. Moreover it is not self-sabilizing solution and a corruption cannot be repaired locally, as noticed by Knuth (1976).

The full version of the paper is available in [6].

This work was supported in part by grants from Digiteo France and by the Israeli ministry of Science and Technology.