Abstract
We present a uniform self-stabilizing algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of an arbitrary positively real-weighted graph. Our algorithm consists in two stages of stabilizing protocols. The first stage is a uniform randomized stabilizing unique naming protocol, and the second stage is a stabilizing MDST protocol, designed as a fair composition of Merlin-Segall's stabilizing protocol and a distributed deterministic stabilizing protocol solving the (MDST) problem. The resulting randomized distributed algorithm presented herein is a composition of the two stages; it stabilizes in O(nΔ+D 2+n log log n) expected time, and uses O(n 2logn+nlogW) memory bits (where n is the order of the graph, Δ is the maximum degree of the network, D is the diameter in terms of hops, and W is the largest edge weight). To our knowledge, our protocol is the very first distributed algorithm for the (MDST) problem. Moreover, it is fault-tolerant and works for any anonymous arbitrary network.
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References
Y. Afek and G. Brown. Self-stabilization of the alternating-bit protocol. In Proc. Symp. Reliable Distr. Syst., pages 80–83, 1989.
E. Anagnostou, R. El-Yaniv, and V. Hadzilacos. Memory adaptative self-stabilizing protocols. In Proc. WDAG, pages 203–220, 1992.
B. Awerbuch. Optimal distributed algorithms for minimum 0weight spanning tree, counting, leader election and related problems. In Proc. ACM STOC, pages 230–240, 1987.
B. Awerbuch, I. Cidon, and S. Kutten. Communication-optimal maintenance of replicated information. In Proc. IEEE FOCS, pages 492–502, 1990.
B. Awerbuch, S. Kutten, Y. Mansour, B. Patt-Shamir, and G. Varghese. Time optimal self-stabilizing synchronization. In Proc. ACM STOC, 1993.
B. Awerbuch, B. Patt-Shamir, G. Varghese, and S. Dolev. Self-stabilization by local checking and global reset. In Proc. WDAG, pages 326–339, 1994.
M. Bui and F. Butelle. Minimum diameter spanning tree. In OPOPAC Proc, Int. Workshop on Principles of Parallel Computing, pages 37–46. Hermès & Inria, Nov. 1993.
F. Butelle, C. Lavault, and M. Bui. A uniform self-stabilizing minimum diameter spanning tree algorithm. RR 95-07, LIPN, University of Paris-Nord, May 1995.
P. M. Camerini, G. Galbiati, and F. Maffioli. Complexity of spanning tree problems: Part I. Europ. J. Oper. Research, 5:346–352, 1980.
N. Christophides. Graph Theory: An algorithmic approach. Computer Science and Applied Mathematics. Academic press, 1975.
E. W. Dijkstra. Self-stabilizing systems in spite of distributed control. CACM, 17(11):643–644, 1974.
S. Dolev, A. Israeli, and S. Moran. Resource bounds on self-stabilizing message driven protocols. In Proc. ACM PODC, 1991.
S. Dolev, A. Israeli, and S. Moran. Uniform dynamic self-stabilizing leader election Part 1: Complete graph protocols. In Proc. WDAG, 1991.
S. Dolev, A. Israeli, and S. Moran. Self-stabilization of dynamic systems assuming read/write atomicity. Distributed Computing, 7(1):3–16, 1993.
S. Dolev, A. Israeli, and S. Moran. Uniform self-stabilizing leader election Part 2: General graph protocol. Technical report, Technion — Israel, Mar. 1995.
S. Dolev. Optimal Time Self-Stabilization in Uniform Dynamic Systems. In Proc. 6th IASTED Int. Conf. on Parallel and Distributed Computing and Systems, 1994.
D. Eppstein, G. F. Italiano, R. Tamassia, R. E. Tarjan, J. Westbrook, and M. Yung. Maintenance of a minimum spanning forest in a dynamic plane graph. J. Algo., 13:33–54, 1992.
R. G. Gallager, P. A. Humblet, and P. M. Spira. A distributed algorithm for minimum weight spanning trees. TOPLAS, 5(1):66–77, 1983.
J.-M. Ho, D. T. Lee, C.-H. Chang, and C. K. Wong. Minimum diameter spanning trees and related problems. SIAM J. Comput., 20(5):987–997, Oct. 1991.
E. Ihler, G. Reich, and P. Wildmayer. On shortest networks for classes of points in the plane. In Int. Workshop on Comp. Geometry — Meth., Algo. and Applic., LNCS, pages 103–111, Mar. 1991.
S. Katz and K. J. Perry. Self-stabilizing extensions for message-passing systems. Distributed Computing, 7(17–26), 1993.
C. Lavault. Évaluation des algorithmes distribués: analyse, complexité, méthode. Hermès, 1995.
P. M. Merlin and A. Segall. A failsafe distributed routing protocol. IEEE Trans. Comm., COM-27(9):1280–1287, Sept. 1979.
R. Perlman. Fault-tolerant broadcast of routing information. Computer Networks, 7:395–405, 1983.
S. K. Shukla, D. Rosenkrantz, and S. S. Ravi. Observations on self-stabilizing graph algorithm for anonymous networks. Technical report, University of Albany, NY, 1995.
G. Varghese. Self-stabilization by counter flushing. In Proc. ACM PODC, pages 244–253, 1994.
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Butelle, F., Lavault, C., Bui, M. (1995). A uniform self-stabilizing minimum diameter spanning tree algorithm. In: Hélary, JM., Raynal, M. (eds) Distributed Algorithms. WDAG 1995. Lecture Notes in Computer Science, vol 972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022152
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DOI: https://doi.org/10.1007/BFb0022152
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