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Research results

Group : Parallel Systems

Asynchronous Self-stabilizing Stable Marriage

Starts on 01/10/2015
Advisor : BEAUQUIER, Joffroy

Funding :
Affiliation : vide
Laboratory : LRI, salle des thèses

Defended on 30/09/2020, committee :
- Johanne Cohen, Présidente du Jury
Directrice de Recherche, Université Paris-Saclay (LRI)

- Colette Johnen, Rapporteure & Examinatrice
Professeure, Université Bordeaux (LaBRI)

- Volker Turau, Rapporteur & Examinateur
Professeur, Hamburg University of Technology (Institut für Telematik)

- Hugues Fauconnier, Examinateur
Professeur, Université de Paris (IRIF)

- Sébastien Tixeuil, Examinateur
Professeur, Sorbonne Université (LIP6)

- Joffroy Beauquier, Directeur de thèse
Professeur émérite, Université Paris-Saclay (LRI)

- Thibault Bernard, Co-encadrant
Maître de conférences, Université de Reims (Li-PaRAD, UP-Saclay)

- Janna Burman, Co-encadrante
Maîtresse de conférences, Université Paris-Saclay (LRI)

Research activities :

Abstract :
The Stable Marriage Problem (SMP) is a matching problem where participants have preferences over their potential partners. The objective is to find a matching that is optimal (stable in certain sens) with regard to these preferences. This type of matching has a lot of widely used applications such as the assignment of children to schools, interns to hospitals, kidney transplant patients to donors, as well as taxi scheduling or content delivery on the Internet. Some applications can be solved in a centralized way while others, due to their distributed nature and their complex data, need a different treatment.

In order to handle this challenge, we provide two distributed self-stabilizing solutions (i.e., that tolerate transient (or short-lived) failures (e.g., memory or message corruptions) of any nodes. The privacy of the preference lists is guaranteed by the two proposed algorithms: lists are not shared, only some binary queries and responses are transmitted.
For both algorithms, executions proceed in atomic steps and a daemon (distributed unfair daemon) conveys the notion of asynchrony. Under this daemon, the stabilization time can be bounded in term of moves (local computations). This complexity metrics allows to evaluate the necessary computational power or the energy consumption of the algorithm's executions.

The first algorithm, based on the centralized method of Ackermann et al. (SICOMP' 2011), solves the problem in O(n^4) moves.

The starting point of the second algorithm is the local detection/global correction scheme of Awerbuch et al. (DA' 1994)
Unfortunately, local checkability definition of DA '1994 does not apply to our case (in particular due to the unfair daemon).
Consequently, we propose a new definition.
Furthermore, we design a distributed self-stabilizing asynchronous reset algorithm.
Using it, the resulting composed algorithm solves SMP in Theta(n^2) moves in a self-stabilizing way.