Time Efficient Self stabilizing Stable Marriage
"Stable marriage" refers to a particular matching with constraints, in troduced in the economic context of two sided markets. The problem has a wide variety of other applications in different domains, such as Cloud computing, Internet content delivery or college admissions. Most of the solutions known up to now are given for the synchronous model, in which executions proceed in rounds, and assume initialization. In this paper, we consider a distributed and asynchronous context, without initializa tion (i.e. in a self stabilizing manner tolerating any transient faults) and with some confidentiality requirements. The single already known self stabilizing solution [24] based on Ackerman et al.'s algorithm [1] is in O(n 4 moves (activation of a single node) We considerably im prove on this previous result by presenting a solution with an complexity of O(n 2 moves (and O(n 2 asynchronous rounds) relying on Gale and Shapley's algorithm [14] This algorithm runs also in O(n 2 moves, but in a centralized synchronous context. Moreover it is not self sabilizing and a corruption cannot be repaired locally, as noticed by Knuth [21]