A randomized competitive algorithm for evaluating priced AND/OR trees

Recently, Charikar et al. investigated the problem of evaluating AND/OR trees, with non-uniform costs on its leaves, from 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 proved 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 take a step towards solving this problem by presenting a -competitive randomized polynomial time algorithm. This contrasts with the best known lower bound μ(T)/2.