Computation in faulty stars [hypercube networks]

The question of simulating a completely healthy hypercube with a degraded one (one with some faulty processors) has been considered by several authors. We consider the question for the star-graph interconnection network. With suitable assumptions on the fault probability, there is, with high probability, a bounded distance embedding of K/sub n/spl times/S/sub n-1/ in a degraded S/sub n/, of congestion O(n). By a different method, a congestion O(log(n)) embedding of S, can be obtained. For the hypercube O(1) congestion has been obtained, but this is open for the star graph. Other results presented include a guaranteed O(n) slowdown simulation if there are sufficiently few faults, and upper and lower bounds for the minimal size of a system of faults rendering faulty every m-substar.<
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