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Issue No.01 - January-February (2011 vol.8)
pp: 1-12
Beat Gfeller , ETH Zurich, Zurich
Nicola Santoro , Carleton University, Ottawa
Peter Widmayer , ETH Zurich, Zurich
ABSTRACT
Communication in networks suffers if a link fails. When the links are edges of a tree that has been chosen from an underlying graph of all possible links, a broken link even disconnects the network. Most often, the link is restored rapidly. A good policy to deal with this sort of transient link failures is swap rerouting, where the temporarily broken link is replaced by a single swap link from the underlying graph. A rapid replacement of a broken link by a swap link is only possible if all swap links have been precomputed. The selection of high-quality swap links is essential; it must follow the same objective as the originally chosen communication subnetwork. We are interested in a minimum-diameter tree in a graph with edge weights (so as to minimize the maximum travel time of messages). Hence, each swap link must minimize (among all possible swaps) the diameter of the tree that results from swapping. We propose a distributed algorithm that efficiently computes all of these swap links, and we explain how to route messages across swap edges with a compact routing scheme. Finally, we consider the computation of swap edges in an arbitrary spanning tree, where swap edges are chosen to minimize the time required to adapt routing in case of a failure, and give efficient distributed algorithms for two variants of this problem.
INDEX TERMS
Fault-tolerant routing, swap edges, minimum-diameter spanning tree, distributed algorithms.
CITATION
Beat Gfeller, Nicola Santoro, Peter Widmayer, "A Distributed Algorithm for Finding All Best Swap Edges of a Minimum-Diameter Spanning Tree", IEEE Transactions on Dependable and Secure Computing, vol.8, no. 1, pp. 1-12, January-February 2011, doi:10.1109/TDSC.2009.17
REFERENCES
[1] B. Gfeller, N. Santoro, and P. Widmayer, "A Distributed Algorithm for Finding All Best Swap Edges of a Minimum Diameter Spanning Tree," Proc. 21st Int'l Symp. Distributed Computing (DISC), pp. 268-282, 2007.
[2] M. Bui, F. Butelle, and C. Lavault, "A Distributed Algorithm for Constructing a Minimum Diameter Spanning Tree," J. Parallel and Distributed Computing, vol. 64, pp. 571-577, 2004.
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[4] E. Nardelli, G. Proietti, and P. Widmayer, "Finding All the Best Swaps of a Minimum Diameter Spanning Tree under Transient Edge Failures," J. Graph Algorithms and Applications, vol. 5, no. 5, pp. 39-57, 2001.
[5] E. Nardelli, G. Proietti, and P. Widmayer, "Swapping a Failing Edge of a Single Source Shortest Paths Tree Is Good and Fast," Algorithmica, vol. 35, no. 1, pp. 56-74, 2003.
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[7] P. Flocchini, A. Mesa Enriques, L. Pagli, G. Prencipe, and N. Santoro, "Point-of-Failure Shortest-Path Rerouting: Computing the Optimal Swap Edges Distributively," IEICE Trans. Information and Systems, vol. E89-D, no. 2, pp. 700-708, 2006.
[8] P. Flocchini, L. Pagli, G. Prencipe, N. Santoro, and P. Widmayer, "Computing All the Best Swap Edges Distributively," J. Parallel and Distributed Computing, vol. 68, no. 7, pp. 976-983, 2008.
[9] F.T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays $\cdot$ Trees $\cdot$ Hypercubes. Morgan Kaufmann Publishers, Inc., 1992.
[10] N. Santoro, Design and Analysis of Distributed Algorithms, Wiley, 2007.
[11] N. Santoro and R. Khatib, "Labelling and Implicit Routing in Networks," The Computer Journal, vol. 28, no. 1, pp. 5-8, 1985.
[12] M. Thorup and U. Zwick, "Compact Routing Schemes," Proc. 13th Ann. ACM Symp. Parallel Algorithms and Architectures (SPAA '01), pp. 1-10, 2001.
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