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<p><b>Abstract</b>—In this paper, we develop algorithms in order of efficiency for all-to-all broadcast problem in an <it>N</it> = 2<super><it>n</it></super>-node <it>n</it>-dimensional faulty SIMD hypercube, <it>Q</it><sub><it>n</it></sub>, with up to <it>n</it><tmath>$-$</tmath> 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 <it>n</it>α + (2<it>N</it><tmath>$-$</tmath> 3)<it>L</it>β in a faulty hypercube with at most <it>n</it><tmath>$-$</tmath> 1 faults (each node has a value of <it>L</it> bytes). Our best algorithm requires 2<it>n</it>α + 2<it>NL</it>β 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.</p>
SIMD hypercube, fault tolerance, dimension ordering, all-to-all broadcast, broadcast, global sum, matrix multiplication.
Amit Sengupta, C.s. Raghavendra, "All-To-All Broadcast and Matrix Multiplication in Faulty SIMD Hypercubes", IEEE Transactions on Parallel & Distributed Systems, vol. 9, no. , pp. 550-560, June 1998, doi:10.1109/71.689442
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