Paradigms Admitting Superunitary Behaviour in Parallel Computation

The phenomenon of a disproportionate decrease in execution time of p2 over p1 processors executing a task in parallel, where p2 > p1, is referred to as superunitary speedup. An analogous phenomenon that we call superunitary ‘success ratio’ occurs in dealing with tasks that can either succeed or fail, when there is a disproportionate increase in the success of p2 over p1 processors. We identify a range of conditions which may lead to superunitary speedup or superunitary success ratio, and propose several new paradigms for problems which admit such superunitary behaviour. Our results suggest that a new theory of parallel computation may be required to accommodate these new paradigms.

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