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

In this paper, we develop algorithms in order of efficiency for all-to-all broadcast problem in an N=2/sup n/-node n-dimensional faulty SIMD hypercube, Q/sub n/, with up to n-1 node faults. The algorithms use a property of a certain ordering of dimensions. Our analysis includes startup time (/spl alpha/) and transfer time (/spl beta/). We have established the lower bound for such an algorithm to be n/spl alpha/+(2N-3)L/spl beta/ in a faulty hypercube with at most n-1 faults (each node has a value of L bytes). Our best algorithm requires 2n/spl alpha/+2NL/spl beta/ 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.