Abstract
The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol.
We present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Second, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date.
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References
Katz, S., Perry, K.J.: Self-stabilizing extensions for message-passing systems. Distributed Computing 7, 17–26 (1993)
Anagnostou, E., Hadzilacos, V.: Tolerating transient and permanent failures (extended abstract). In: Schiper, A. (ed.) WDAG 1993. LNCS, vol. 725, pp. 174–188. Springer, Heidelberg (1993)
Ben-Or, M., Dolev, D., Hoch, E.N.: Fast self-stabilizing byzantine tolerant digital clock synchronization. In: Bazzi, R.A., Patt-Shamir, B. (eds.) PODC, pp. 385–394. ACM Press, New York (2008)
Cobb, J.A., Gouda, M.G.: Stabilization of general loop-free routing. J. Parallel Distrib. Comput. 62(5), 922–944 (2002)
Datta, A.K., Gurumurthy, S., Petit, F., Villain, V.: Self-stabilizing network orientation algorithms in arbitrary rooted networks. Stud. Inform. Univ. 1(1), 1–22 (2001)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)
Dolev, S.: Self-stabilization. MIT Press, Cambridge (2000)
Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)
Dolev, S., Herman, T.: Superstabilizing protocols for dynamic distributed systems. Chicago J. Theor. Comput. Sci. (1997)
Dolev, S., Welch, J.L.: Wait-free clock synchronization. Algorithmica 18(4), 486–511 (1997)
Dolev, S., Welch, J.L.: Self-stabilizing clock synchronization in the presence of byzantine faults. J. ACM 51(5), 780–799 (2004)
Gafni, E.M., Bertsekas, P.: Distributed algorithms for generating loop-free routes in networks with frequently changing topology. IEEE Transactions on Communications 29, 11–18 (1981)
Gallager, R.G., Humblet, P.A., Spira, P.M.: A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst. 5(1), 66–77 (1983)
Garcia-Luna-Aceves, J.J.: Loop-free routing using diffusing computations. IEEE/ACM Trans. Netw. 1(1), 130–141 (1993)
Gopal, A.S., Perry, K.J.: Unifying self-stabilization and fault-tolerance (preliminary version). In: PODC, pp. 195–206 (1993)
Gouda, M.G., Herman, T.: Adaptive programming. IEEE Trans. Software Eng. 17(9), 911–921 (1991)
Gouda, M.G., Schneider, M.: Stabilization of maximal metric trees. In: Arora, A. (ed.) WSS, pp. 10–17. IEEE Computer Society Press, Los Alamitos (1999)
Gupta, S.K.S., Srimani, P.K.: Self-stabilizing multicast protocols for ad hoc networks. J. Parallel Distrib. Comput. 63(1), 87–96 (2003)
Higham, L., Liang, Z.: Self-stabilizing minimum spanning tree construction on message-passing networks. In: Welch, J.L. (ed.) DISC 2001. LNCS, vol. 2180, pp. 194–208. Springer, Heidelberg (2001)
Johnen, C., Tixeuil, S.: Route Preserving Stabilization. In: Huang, S.-T., Herman, T. (eds.) SSS 2003. LNCS, vol. 2704, pp. 184–198. Springer, Heidelberg (2003)
Johnen, C., Tixeuil, S.: Route preserving stabilization. In: Self-Stabilizing Systems, pp. 184–198 (2003)
Kruskal, J.B.: On the shortest spanning subtree of a graph and the travelling salesman problem. Proc. Amer. Math. Soc. 7, 48–50 (1956)
Papatriantafilou, M., Tsigas, P.: On self-stabilizing wait-free clock synchronization. Parallel Processing Letters 7(3), 321–328 (1997)
Petit, F., Villain, V.: Optimal snap-stabilizing depth-first token circulation in tree networks. J. Parallel Distrib. Comput. 67(1), 1–12 (2007)
Prim, R.C.: Shortest connection networks and some generalizations. Bell System Tech. J., 1389–1401 (1957)
Sleator, D.D., Tarjan, R.E.: A data structure for dynamic trees. J. Comput. Syst. Sci. 26(3), 362–391 (1983)
Blin, L., Potop-Butucaru, M.G., Rovedakis, S., Tixeuil, S.: A new self-stabilizing minimum spanning tree construction with loop-free property. Research Report, inria-00384041, INRIA (2009)
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Blin, L., Potop-Butucaru, M., Rovedakis, S., Tixeuil, S. (2009). A New Self-stabilizing Minimum Spanning Tree Construction with Loop-Free Property. In: Keidar, I. (eds) Distributed Computing. DISC 2009. Lecture Notes in Computer Science, vol 5805. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04355-0_43
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DOI: https://doi.org/10.1007/978-3-642-04355-0_43
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