Time Efficient Self-stabilizing Stable Marriage
Abstract
“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].
Origin : Files produced by the author(s)
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