The Complexity of Algorithms Computing Game Trees on Random Assignments

Abstract

The complexity of algorithms for computing game trees on random assignments has been given substantial attention in the literature. In this line, we investigate the complexity of algorithms that compute a special class of game trees $T_{2}^{k}$ from a new perspective — eigen-distribution. This particular distribution is defined as the worst distribution on assignments to variables of $T_{2}^{k}$ regarding a best algorithm. In this paper, we show the eigen-distribution on assignments for $T_{2}^{k}$ in two separate cases, where the assignments to leaves are independently distributed (ID) and correlated distributed(CD). Then we use eigen-distribution to derive the tight bound of the complexity of algorithms for $T_{2}^{k}$.