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The paper summarizes recent analytical investigations of the mathematical properties of heuristics and their influence on the performance of common search techniques. The results are reported without proofs together with discussions of motivations and interpretations. The highlights include the following: the optimality of A*; relations between the precision of the heuristic estimates and the average complexity of the search; comparisons of the average complexities of A* and BACKTRACKING; procedures for comparing and combining nonadmissible heuristic functions; the influence of the weight w (in f = (l - w) g + wh) on the complexity of A*; the pruning power of alphabeta, SSS*, and SCOUT; the effect of successor ordering on search complexity, and the effect of search depth of the quality of decisions in game-playing.
Judea Pearl (Sun,) studied this question.