A randomized competitive algorithm for evaluating priced AND/OR trees

Abstract

Recently, Charikar et. al. investigated the problem of evaluating AND/OR trees, with non uniform costs on its leaves, under the perspective of the competitive analysis. For an AND-OR tree T they presented a μ(T)-competitive deterministic polynomial time algorithm, where μ(T) is the number of leaves that must be read, in the worst case, in order to determine the value of T. Furthermore, they prove that μ(T) is a lower bound on the deterministic competitiveness, which assures the optimality of their algorithm. The power of randomization in this context has remained as an open question. Here, we give a step towards solving this problem by presenting a 0.792μ(T)-competitive randomized polynomial time algorithm. This contrasts with the best known lower bound μ(T)/2. © Springer-Verlag 2004.