Reconfiguration of Spanning Trees in Faulty Hypercubes

Spanning trees have been used extensively in algorithms for hypercube communications and broadcasting. We present algorithms for reconnecting spanning trees and achieving communication among the nonfaulty nodes in the hypercube. The algorithms presented provide reconfiguration for the completely unbalanced spanning tree (CUST), balanced spanning tree (BST), and general spanning tree (GST) in hypercubes in the presence of single node failure. These algorithms can reconfigure around any single fault in 0(1) reconfiguration time with no dilation and will increase the congestion of a link by, at most, one. Simulation results for the algorithms under multiple faults also are presented.

[1]  S. Lennart Johnsson,et al.  Optimum Broadcasting and Personalized Communication in Hypercubes , 1989, IEEE Trans. Computers.

[2]  John N. Tsitsiklis,et al.  Optimal Communication Algorithms for Hypercubes , 1991, J. Parallel Distributed Comput..

[3]  Gurdip Singh,et al.  Reconfiguration of spanning trees in networks in the presence of node failures , 1993, [1993] Proceedings. The 13th International Conference on Distributed Computing Systems.

[4]  Kemal Efe,et al.  Congestion and fault tolerance of binary tree embeddings on hypercube , 1991, [1991] Proceedings. The Fifth International Parallel Processing Symposium.

[5]  Dimiter R. Avresky,et al.  Reconfiguration of Faulty Hypercubes , 1994, EDCC.

[6]  Cauligi S. Raghavendra,et al.  Reconfiguration of binary trees in faulty hypercubes , 1993, [1993] Proceedings Seventh International Parallel Processing Symposium.

[7]  Feng-Hsu Wang,et al.  On Constructing Multiple Spanning Trees in a Hypercube , 1993, Inf. Process. Lett..