Brief Announcement: Time Efficient Self-Stabilizing Stable Marriage

"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 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).