A SUBLINEAR-TIME RANDOMIZED APPROXIMATION ALGORITHM FOR MATRIX GAMES

This paper presents a parallel randomized algorithm which computes a pair of epsilon-optimal strategies for a given (m,n)matrix game A = [a(ij)] is an element of [-1, 1] in 0(epsilon(-2) log(2)(n+m)) expected time on an (n+m)/log(n+m)-processor EREW PRAM. For any fixed accuracy epsilon > 0, the expected sequential running time of the suggested algorithm is 0((n + m)log(n + m)), which is sublinear in mn, the number of input elements of A. On the other hand, simple arguments are given to show that for epsilon < 1/2, any deterministic algorithm for computing a pair of epsilon-optimal strategies of an (m, n)-mabix game A with +/-1 elements examines a(mn) of its elements. In particular, for m = n the randomized algorithm achieves an almost quadratic expected speedup relative to any deterministic method.