Recursively divisible problems
We introduce the concept of a (p, d)-divisible problem, where p reflects the number of processors and d the number of communication phases of a parallel algorithm solving the problem. We call problems that are recursively (n∈, O(1))-divisible in a work-optimal way with 0 <ε < 1ideally divisible and give motivation drawn from parallel computing for the relevance of that concept. We show that several important problems are ideally divisible. For example, sorting is recursively (n1/3, 4)-divisible in a work-optimal way. On the other hand, we also provide some results of lower bound type. For example, ideally divisible problems appear to be a proper subclass of the functional complexity class FP of sequentially feasible problems. Finally, we also give some extensions and variations of the concept of (p, d)-divisibility.
KeywordsParallel Algorithm Communication Phase Sorting Problem Proper Subclass Parallel Random Access Machine
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