Abstract
This paper presents a self-stabilizing algorithm to color the edges of a bipartite network such that any two adjacent edges receive distinct colors. The algorithm has the self-stabilizing property; it works without initializing the system. It also works in a de-centralized way without a leader computing a proper coloring for the whole system. Moreover, it finds an optimal edge coloring and its time complexity is O(n 2 k + m) moves, where k is the number of edges that are not properly colored in the initial configuration.
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Burman, J., Kutten, S.: Time optimal asynchronous self-stabilizing spanning tree. In: DISC, pp. 92–107 (2007)
Cole R., Ost K., Schirra S.: Edge-coloring bipartite multigraphs in O(E log D) time. Combinatorica 21(1), 5–12 (2001)
Dijkstra E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17, 643–644 (1974)
Dolev S.: Self-stabilization. MIT Press, Cambridge (2000)
Dolev S., Herman T.: Parallel composition for time-to-fault adaptive stabilization. Distrib. Comput. 20(1), 29–38 (2007)
Dolev S., Israeli A., Moran S.: Self-stabilization of dynamic systems assuming only read/write atomicity. Distrib. Comput. 7(1), 3–16 (1993)
Durand D., Jain R., Tseytlin D.: Parallel I/O scheduling using randomized, distributed edge coloring algorithms. J. Parallel Distrib. Comput. 63, 611–618 (2003)
Gabow, H.N., Kariv, O.: Algorithms for edge coloring bipartite graphs. In: Conference of the 10th Annual ACM Symposium on Theory of Computing, pp. 184–192. ACM Press, New York (1978)
Gabow H.N., Kariv O.: Algorithms for edge coloring bipartite graphs and multigraphs. SIAM J. Comput. 11(1), 117–129 (1982)
Gandham S., Dawande M., Prakash R.: Link scheduling in wireless sensor networks: distributed edge-coloring revisited. J. Parallel Distrib. Comput. 68(8), 1122–1134 (2008)
Grable D., Panconesi A.: Nearly optimal distributed edge-coloring in O(log log n) rounds. RSA 10(3), 385–405 (1997)
Gradinariu, M., Tixeuil, S.: Conflict managers for self-stabilization without fairness assumption. In: ICDCS ’07: Proceedings of the 27th International Conference on Distributed Computing Systems, p. 46. IEEE Computer Society, Washington (2007)
Graham R.L., Knuth D.E., Patashnik O.: Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley Longman Publishing Co., Inc., Boston (1994)
Herman, T., Pirwani, I., Pemmaraju, S.: Oriented edge colorings and link scheduling in sensor networks. In: International Conference on communication Software and Middleware, pp. 1–6 (2006)
Huang, S.T., Tzeng, C.H.: Distributed edge coloration for bipartite networks. In: Stabilization, Safety, and Security of Distributed Systems. LNCS, vol. 4280, pp. 363–377. Springer, Heidelberg (2006)
Katayama Y., Ueda E., Fujiwara H., Masuzawa T.: A latency optimal superstabilizing mutual exclusion protocol in unidirectional rings. J. Parallel Distrib. Comput. 62, 865–884 (2002)
König D.: Über graphen und ihre anwendung auf determinententheorie und mengenlehre. Math. Ann. 77, 453–465 (1916)
Kutten S., Patt-Shamir B.: Stabilizing time-adaptive protocols. Theor. Comput. Sci. 220(1), 93–111 (1999)
Masuzawa T., Tixeuil S.: Stabilizing link-coloration of arbitrary networks with unbounded Byzantine faults. Int. J. Princ. Appl. Inf. Sci. Technol. 1(1), 1–13 (2007)
Masuzawa T., Tixeuil S.: On bootstrapping topology knowledge in anonymous networks. ACM Trans. Auton. Adapt. Syst. 4(1), 1–27 (2009)
Mizuno M., Nesterenko M.: A transformation of self-stabilizing serial model programs for asynchronous parallel computing environments. Inf. Process. Lett. 66(6), 285–290 (1998)
Panconesi A., Srinivasan A.: Fast randomized algorithms for distributed edge coloring. SIAM J. Comput. 26(2), 350–368 (1992)
Rizzi R.: Konig’s edge coloring theorem without augmenting paths. J. Graph Theory 29, 87 (1998)
Sakurai, Y., Ooshita, F., Masuzawa, T.: A self-stabilizing link-coloring protocol resilient to Byzantine faults in tree networks. In: OPODIS, pp. 283–298. Springer, Heidelberg (2004)
Schrijver A.: Bipartite edge coloring in O(Δm) time. SIAM J. Comput. 28, 841–846 (1999)
Tzeng C.H., Jiang J.R., Huang S.T.: A self-stabilizing (Δ+4)-edge-coloring algorithm for planar graphs in anonymous uniform systems. Inf. Process. Lett. 101(4), 168–173 (2007)
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This is a completely revised and extended version of [15]. This research was supported in part by the National Science Council of the Republic of China under the Contract NSC94-2213-E008-001.
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Huang, ST., Tzeng, CH. Distributed edge coloration for bipartite networks. Distrib. Comput. 22, 3–14 (2009). https://doi.org/10.1007/s00446-009-0082-8
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DOI: https://doi.org/10.1007/s00446-009-0082-8