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Edge-Disjoint Spanning Trees on the Star Network with Applications to Fault Tolerance
February 1996 (vol. 45 no. 2)
pp. 174-185

Abstract—Data communication and fault tolerance are important issues in parallel computers in which the processors are interconnected according to a specific topology. One way to achieve fault tolerant interprocessor communication is by exploiting and effectively utilizing the disjoint paths that exist between pairs of source and destination nodes. In this paper, we construct n - 1 directed edge-disjoint spanning trees, on the star network. These spanning trees are used to derive a near optimal single-node broadcasting algorithm, and fault tolerant algorithms for the single-node and multinode broadcasting, and for the single-node and multinode scattering problems. Broadcasting is the distribution of the same group of messages from one processor to all the other processors. Scattering is the distribution of distinct groups of messages from one processor to all the other processors. We consider broadcasting and scattering from a single processor of the network and simultaneously from all processors of the network. The single-node broadcasting algorithm offers a speed up of n - 1 for a large number of messages, over the straightforward algorithm that uses a single shortest path spanning tree. Fault tolerance is achieved by transmitting the same messages through a number of edge-disjoint spanning trees. The fault tolerant algorithms operate successfully in the presence of up to n - 2 faulty nodes or edges in the network. The degree of fault tolerance can be adjusted depending on the network reliability. The importance of this method lies in the fact that no prior knowledge of the faulty nodes or edges is required. All of the algorithms operate under the store-and-forward, all-port communication model.

[1] S.B. Akers, D. Harel, and B. Krishnamurthy, "The star graph: An attractive alternative to the hypercube," Proc. Int'l Conf. Parallel Processing, pp. 393-400, St. Charles, Ill., 1987.
[2] S.B. Akers and B. Krishnamurthy, "The fault tolerance of star graphs," Proc. Int'l Conf. Supercomputing, pp. 270-276,San Francisco, 1987.
[3] S.B. Akers and B. Krishnamurthy, “A Group-Theoretic Model for Symmetric Interconnection Networks,” IEEE Trans. Computers, vol. 38, no. 4, pp. 555-566, Apr. 1989.
[4] P. Berthomé, A. Ferreira, and S. Perennes, "Optimal Information Dissemination in Star and Pancake Networks," Proc. Fifth IEEE Symp. Parallel and Distributed Processing, pp. 720-724, Dec. 1993.
[5] D. Bertsekas, C. Ozveren, G. Stamoulis, P. Tseng, and J. Tsitsiklis, "Optimal Communication Algorithms for Hypercubes," J. Parallel and Distributed Computing, vol. 11, pp. 263-275, 1991.
[6] K. Day and A. Tripathi, "A Comparative Study of Topological Properties of Hypercubes and Star Graphs," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 1, pp. 31-38, Jan. 1994.
[7] M. Dietzfelbinger, S. Madhavapeddy, and I.H. Sudborough, "Three disjoint path paradigms in star networks," Proc. Third IEEE Symp. Parallel and Distributed Processing, pp. 400-406, 1991.
[8] P. Fragopoulou and S.G. Akl, “Optimal Communication Algorithms on Star Graphs Using Spanning Tree Constructions,” J. Parallel and Distributed Computing, vol. 24, pp. 55-71, 1995.
[9] P. Fraigniaud and C.T. Ho, "Arc-disjoint spanning trees on the cube connected cycles network," Proc. Int'l Conf. Parallel Processing, vol. I, pp. 225-229, St. Charles, Ill., 1991.
[10] P. Fraigniaud, "Fault-tolerant gossiping on hypercube multicomputers," Proc. EDMCC2, pp. 463-472, Munich, 1991.
[11] L. Gargano, U. Vaccaro, and A. Vozella, “Fault-Tolerant Routing in the Star and Pancake Interconnection Networks,” Information Processing Letters, vol. 45, pp. 315-320, Apr. 1993.
[12] S.L. Johnsson and C.T. Ho,“Spanning graphs for optimum broadcasting and personalizedcommunication in hypercubes,” IEEE Trans. Computers, vol. 38, no. 9, pp. 1,249-1,268, Sept. 1989.
[13] J. Jwo, S. Lakshmivarahan, and S.K. Dhall, "Characterization of node disjoint (parallel) paths in star graphs," Proc. Int'l Parallel Processing Symp., pp. 404-409,Anaheim, Calif., 1991.
[14] V.E. Mendia and D. Sarkar, “Optimal Broadcasting in the Star Graph,” IEEE Trans. Parallel and Distributed Systems, vol. 3, pp. 389-396, July 1992.
[15] P. Ramanathan and K.G. Shin, "Reliable Broadcast in Hypercube Multicomputers," IEEE Trans. Computers, vol. 37, no. 12, pp. 1,654-1,657, Dec. 1988.

Index Terms:
Communication algorithm, edge-disjoint trees, fault tolerance, interconnection network, parallel algorithm, spanning tree, star network.
Citation:
Paraskevi Fragopoulou, Selim G. Akl, "Edge-Disjoint Spanning Trees on the Star Network with Applications to Fault Tolerance," IEEE Transactions on Computers, vol. 45, no. 2, pp. 174-185, Feb. 1996, doi:10.1109/12.485370
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