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All-To-All Broadcast and Matrix Multiplication in Faulty SIMD Hypercubes
June 1998 (vol. 9 no. 6)
pp. 550-560

Abstract—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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Index Terms:
SIMD hypercube, fault tolerance, dimension ordering, all-to-all broadcast, broadcast, global sum, matrix multiplication.
Citation:
Amit Sengupta, C.s. Raghavendra, "All-To-All Broadcast and Matrix Multiplication in Faulty SIMD Hypercubes," IEEE Transactions on Parallel and Distributed Systems, vol. 9, no. 6, pp. 550-560, June 1998, doi:10.1109/71.689442
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