Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
Principles of artificial intelligence
Principles of artificial intelligence
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Experiments With Some Programs That Search Game Trees
Journal of the ACM (JACM)
Optimal Search on Some Game Trees
Journal of the ACM (JACM)
Polynomial evaluations of bi-valued game trees
CSC '86 Proceedings of the 1986 ACM fourteenth annual conference on Computer science
The solution for the branching factor of the alpha-beta pruning algorithm and its optimality
Communications of the ACM
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Let each leaf in a bi-valued game tree have the same probability PO of being labeled a WIN. Define a search algorithm D for a bi-valued game tree T to be directed if D consists of searching T by adhering to a predetermined ordering of the leaves of T, an ordering which is independent both of PO and of the assignment of WINs and LOSSes to the leaves of T. The following theorems are established for an arbitrary bi-valued game tree T: (i) An optimal search algorithm for T has a piecewise polynomial cost function V(T) in PO and V(T) is the infimum of the set of all cost functions VA (T) where A ranges over the set of all directed search algorithms. (ii) T has an optimal search algorithm which is directed if and only if it has an optimal search algorithm with a cost function which is a polynomial in PO. (iii) If T has leaves at both even and odd depths from the root, then no optimal algorithm for searching T is directed.