Optimal randomized algorithms of weakly-balanced multi-branching AND-OR trees

Abstract

This article treats AND-OR tree computation in terms of query complexity. We are interested in the cases where assignments (inputs) or algorithms are randomized. For the former case, it is known that there is a unique randomized assignment achieving the distributional complexity of balanced trees. On the other hand, the dual problem has the opposite result; the optimal randomized algorithms for balanced trees are not unique. We extend the latter study on randomized algorithms to weakly-balanced trees, and see that the uniqueness still fails.