Total exchange in faulty SIMD hypercubes

We develop algorithms for performing total exchange (all-to-all broadcast) in an n-dimensional faulty SIMD hypercube, Q/sub n/, with up to n/spl minus/1 node faults. In an SIMD hypercube, during a communication step, nodes can exchange information with their neighbors only across a specific dimension. We describe a sequence of algorithms which take N log N, N log n, 3N/spl minus/7, 2.5N/spl minus/7 steps for this problem. By carefully analyzing these algorithms and a property of certain ordering of dimensions, we obtain an improved algorithm which takes 2N steps.<<ETX>>

[1]  Cauligi S. Raghavendra,et al.  Global semigroup operations in faulty SIMD hypercubes , 1993, [1993] Proceedings Seventh International Parallel Processing Symposium.

[2]  Cauligi S. Raghavendra,et al.  Free Dimensions-An Effective Approach to Achieving Fault Tolerance in Hypercubes , 1995, IEEE Trans. Computers.

[3]  Cauligi S. Raghavendra,et al.  Free dimensions-an effective approach to achieving fault tolerance in hypercube , 1992, [1992] Digest of Papers. FTCS-22: The Twenty-Second International Symposium on Fault-Tolerant Computing.

[4]  Arthur L. Liestman,et al.  A survey of gossiping and broadcasting in communication networks , 1988, Networks.

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

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

[7]  Bernd Becker,et al.  How robust is the n-cube? , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[8]  Cauligi S. Raghavendra,et al.  Broadcasting algorithms in faulty SIMD hypercubes , 1992, [1992] Proceedings of the Fourth IEEE Symposium on Parallel and Distributed Processing.

[9]  Pierre Fraigniaud,et al.  Asymptotically Optimal Broadcasting and Gossiping in Faulty Hypercube Multicomputers , 1992, IEEE Trans. Computers.

[10]  Jehoshua Bruck,et al.  Running algorithms efficiently on faulty hypercubes , 1990, SPAA '90.

[11]  Cauligi S. Raghavendra,et al.  Prefix Computation on a Faulty Hypercube , 1993, 1993 International Conference on Parallel Processing - ICPP'93.

[12]  Parameswaran Ramanathan,et al.  Reliable Broadcast in Hypercube Multicomputers , 1988, IEEE Trans. Computers.