Abstract
Interval allocation has been suggested as a possible formalization for the PRAM of the (vaguely defined) processor allocation problem, which is of fundamental importance in parallel computing. The interval allocation problem is, given n nonnegative integers x1, ., xn, to allocate n nonoverlapping subarrays of sizes x1, ., xn from within a base array of O(Σnj=1xj) cells. We show that interval allocation problems of size n can be solved in O((log log n)3) time with optimal speedup on a deterministic CRCW PRAM. In addition to a general solution to the processor allocation problem, this implies an improved deterministic algorithm for the problem of approximate summation. For both interval allocation and approximate summation, the fastest previous deterministic algorithms have running times of Θ(log n/log log n). We describe an application to the problem of computing the connected components of an undirected graph. Finally we show that there is a nonuniform deterministic algorithm that solves interval allocation problems of size n in O(log log n) time with optimal speedup.
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