On parallel evaluation of game trees
Journal of the ACM (JACM)
The variance of two game tree algorithms
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Query strategies for priced information (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Query strategies for priced information
Journal of Computer and System Sciences - Special issue on STOC 2000
A randomized competitive algorithm for evaluating priced AND/OR trees
Theoretical Computer Science
| Hi-index | 0.00 |
It was shown that the expected number of leaves evaluated by randomized $\alpha - \beta$ search for evaluating uniform game trees of degree $d$ and height $h$ is $O((B_d)^h)$ where $B_d = d/2+\ln d+O(1)$. It was shown by Saks and Wigderson [Proceedings of 27th Annual Symposium on Foundations of Computer Science (1986), pp. 29-38] that the optimal branching factor of randomized algorithms for evaluating uniform trees of degree $d$ is $B^{\ast}_d= (d-1+\sqrt{d^2+14d+1}\,)/4= d/2+O(1)$. As $B_d/B^{\ast}_d=1+O(\ln d/d)$, randomized $\alpha$-$\beta$ search is asymptotically optimal for evaluating uniform game trees as the degree of tree increases.