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All-to-all broadcast and matrix multiplication in faulty SIMD hypercubes

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2 Author(s)
Sengupta, A. ; Oracle Corp., Redwood Shores, CA, USA ; Raghavendra, C.S.

In this paper, we develop algorithms in order of efficiency for all-to-all broadcast problem in an N=2n-node n-dimensional faulty SIMD hypercube, Qn, with up to n-1 node faults. The algorithms use a property of a certain ordering of dimensions. Our analysis includes startup time (α) and transfer time (β). We have established the lower bound for such an algorithm to be nα+(2N-3)Lβ in a faulty hypercube with at most n-1 faults (each node has a value of L bytes). Our best algorithm requires 2nα+2NLβ and is near-optimal. We develop an optimal algorithm for matrix multiplication in a faulty hypercube using all-to-all broadcast and compare the efficiency of all-to-all broadcast approach with broadcast approach and global sum approach for matrix multiplication. The algorithms are congestion-free and applicable in the context of available hypercube machines

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:9 ,  Issue: 6 )