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Self-stabilization in preference-based systems

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Abstract

Participants of a decentralized system often use some local ranking informations, for selection of effective collaborations. We say that such systems are preference-based. For most practical types of preferences, such systems converge towards a unique stable configuration. In this paper, we investigate the speed and quality of the convergence process with respect to the model parameters. Our results provide an interesting insight into the design of system parameters, such as the number of connections or the algorithm for choosing new partners.

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Notes

  1. The sign of the inequality is arbitrary. If marks stand for bandwidths, higher marks are preferred; if they mean latencies, lower marks are preferred; in this paper, we suppose w.l.o.g. that lower marks are preferred.

  2. Remark: the initiative concept originally comes from this DA algorithm.

  3. One can indeed prove that if G(s) admit at least one edge, the configuration is not stable (see for instance [21]).

  4. Of course, we have empirically verified that H S(k) is well centered around its mean, which is the necessary condition to use Conjecture 1.

  5. Gai et al. showed that symmetric marks can define all possible acyclic preferences, including global preferences [8]. Therefore it is natural to consider how close to global preferences a symmetric matrix is.

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  1. Orange Labs, 38-40 rue du général Leclerc, 92794, Issy-les-Moulineaux, France

    Fabien Mathieu

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Mathieu, F. Self-stabilization in preference-based systems. Peer-to-Peer Netw. Appl. 1, 104–121 (2008). https://doi.org/10.1007/s12083-008-0009-3

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