论文信息 - Upper Bounds for Stabilization in Acyclic Preference-Based Systems

Upper Bounds for Stabilization in Acyclic Preference-Based Systems

Preference-based systems (p.b.s.) describe interactions between nodes of a system that can rank their neighbors. Previous work has shown that p.b.s. converge to a unique locally stable matching if an acyclicity property is verified. In the following we analyze acyclic p.b.s. with respect to the self-stabilization theory. We prove that the round complexity is bounded by n/2 for the adversarial daemon. The step complexity is equivalent to n2/4 for the round robin daemon, and exponential for the general adversarial daemon.

Fabien Mathieu | F. Mathieu

[1] David Manlove,et al. The Hospitals/Residents Problem with Ties , 2000, SWAT.

[2] Laurent Viennot,et al. Acyclic Preference Systems in P2P Networks , 2007, Euro-Par.

[3] Fabien Mathieu,et al. Stratification in P2P Networks: Application to BitTorrent , 2006, ICDCS.

[4] Alvin E. Roth,et al. Pairwise Kidney Exchange , 2004, J. Econ. Theory.

[5] Edsger W. Dijkstra,et al. Self-stabilizing systems in spite of distributed control , 1974, CACM.

[6] Richard Bellman,et al. Asymptotic behavior of solutions of differential-difference equations , 1959 .

[7] Adolf Hildebrand. The Asymptotic Behavior of the Solutions of a Class of Differential‐Difference Equations , 1990 .

[8] Fabien Mathieu. Self-Stabilization in Preference-Based Networks , 2007, Seventh IEEE International Conference on Peer-to-Peer Computing (P2P 2007).

[9] Laurent Viennot,et al. On Using Matching Theory to Understand P2P Network Design , 2006, ArXiv.

[10] David Manlove,et al. The Stable Roommates Problem with Ties , 2002, J. Algorithms.

[11] Shlomi Dolev,et al. Self Stabilization , 2004, J. Aerosp. Comput. Inf. Commun..

[12] A. Roth. The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory , 1984, Journal of Political Economy.