Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
A Self-stabilizing Algorithm for Maximum Popular Matching of Strictly Ordered Preference Lists

Authors: Zhengnan Shi

Abstract:

In this paper, we consider the problem of Popular Matching of strictly ordered preference lists. A Popular Matching is not guaranteed to exist in any network. We propose an IDbased, constant space, self-stabilizing algorithm that converges to a Maximum Popular Matching an optimum solution, if one exist. We show that the algorithm stabilizes in O(n5) moves under any scheduler (daemon).

Keywords: self-stabilization, popular matching, algorithm, distributed computing, fault tolerance

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079514

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 823

References:


[1] D. J. Abraham, R. W. Irving, T. Kavitha, and K. Mehlhorn. Popular matchings. SIAM J. Comput., 37(4):1030-1045, 2007.
[2] J. Beauquier, A. K. Datta, M. Gradinariu, and F. Magniette. Selfstabilizing local mutual exclusion and daemon refinement. In International Symposium on Distributed Computing, pages 223-237, 2000.
[3] E. W. Dijkstra. Self-stabilizing systems in spite of distributed control. Comm. ACM, 17(11):643-644, Jan. 1974.
[4] S. Dolev. Self-Stabilization. MIT Press, 2000.
[5] S. Dolev, A. Israeli, and S. Moran. Uniform dynamic self-stabilizing leader election. IEEE Trans. on Parallel and Distributed Systems, 8(4), 1995.
[6] D. Gale and L. S. Shapley. College admissions and the stability of marriage. American Mathematical Monthly, 69:9-15, 1962.
[7] P. Gardenfors. Match making: assignments based on bilateral preferences. Behavioral Sciences, 20:166-173, 1975.
[8] D. Gusfield and R. W. Irving. The Stable Marriage Problem: Structure and Algorithms. MIT Press, 1989.
[9] P. Hall. On representatives of subsets. Journal of the London Mathematical Society, 10:26-30, 1935.
[10] S. M. Hedetniemi, S. T. Hedetniemi, D. P. Jacobs, and P. K. Srimani. Self-stabilizing algorithms for minimal dominating sets and maximal independent sets. Comput. Math. Appl., 46(5-6):805-811, 2003.
[11] S.-C. Hsu and S.-T. Huang. A self-stabilizing algorithm for maximal matching. Inform. Process. Lett., 43:77-81, 1992.
[12] A. Panconesi and A. Srinivasan. The local nature of -coloring and its algorithmic applications. Combinatorica, 15:225-280, 1995.
[13] S. Rajagopalan and V. Vazirani. Primal-dual RNC approximation algorithms for set cover and covering integer programs. SIAM J. Comput., 28:525-540, 1998.
[14] Z. Shi, W. Goddard, and S. T. Hedetniemi. an anonymous selfstabilizing algorithm for 1-maximal independent set in trees. Information Processing Letters, 91(2):77-83, 2004.
[15] G. Tel. Introduction to Distributed Algorithms, Second Edition. Cambridge University Press, Cambridge UK, 2000.