An optimal sublinear time parallel algorithm for some dynamic programming problems

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Abstract

We consider the following problem: minimize the time of optimal parallel computations of a dynamic programming problem given by dynamic programming recurrences. By an optimal algorithm we mean here the algorithm whose total work matches the work of the best known sequential algorithm for a given problem (in this case O(n3) ). We construct an optimal parallel algorithm which runs in time O(n23logn) with total work O(n 3). It is presently the fastest optimal algorithm for the general dynamic programming recurrences. A preliminary version (with a weaker result) of this paper was presented as a part of [10].

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