An optimal sublinear time parallel algorithm for some dynamic programming problems

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( n 3) ). We construct an optimal parallel algorithm which runs in time O(n 2 3 logn) 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].