A Highly - Parallel Alpha - Beta Algorithm

A new parallel formulation of the alpha-beta algorithm for minimax game tree searching is presented. Its chief characteristic is incremental information sharing among subsearch processes in the form of "provisional" node value communica tion. Such "eager" communication can offer the double benefit of faster search focusing and enhanced parallelism. This effect is particularly advantageous in the prevalent case when static value correlation exists among adjacent nodes. A message-passing formulation of this idea, termed the "Key Node Method", is outlined. Preliminary exper imental resul ts for this method are reported, supporting its validity and potential for increased speedup. This work has supported in part by the National Science Foundation under grant HCS 78-03832. 1. The alpha-beta algorithm 1.1. Review The alpha-beta strategy is a familiar method for economizing on the cost of minimax searching on game trees. Under this strategy, move generation at a node is "cut-off" or abandoned whenever it is determined from nearby node values that the node's ultimate value cannot possibly rise to the root of the tree. Such cuts may be "shallow" (due to a superior sibling), or "deep" (due to a superior ancestor sibling). Although the alpha-beta strategy has at times been called a heuristic, it is rather an optimization admitting no possibility of error in top-level minimax move selection. A number of studies have estimated the savings obtained by the alpha-beta strategy under vc.rious conditions (e.g. [13J). In sum, these findings indicate that the alpha-beta strategy significantly slows (but does not eliminate) the exponential cost of searching to increasing game tree depths. In view of its ease of implementation in ordinary (i.e. recursive) depth-first searching, the method has seen