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This paper reports several properties of heuristic best-first search strategies whose scoring functions ƒ depend on all the information available from each candidate path, not merely on the current cost g and the estimated completion cost h . It is shown that several known properties of A* retain their form (with the minmax of f playing the role of the optimal cost), which helps establish general tests of admissibility and general conditions for node expansion for these strategies. On the basis of this framework the computational optimality of A*, in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that A* uses, is examined. A hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered. Computational performances relative to these algorithms and domains are appraised. For each class-domain combination, we then identify the strongest type of optimality that exists and the algorithm for achieving it. The main results of this paper relate to the class of algorithms that, like A*, return optimal solutions (i.e., admissible) when all cost estimates are optimistic (i.e., h ≤ h *). On this class, A* is shown to be not optimal and it is also shown that no optimal algorithm exists, but if the performance tests are confirmed to cases in which the estimates are also consistent, then A* is indeed optimal. Additionally, A* is also shown to be optimal over a subset of the latter class containing all best-first algorithms that are guided by path-dependent evaluation functions.

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Probabilistic inference algorithms for find ing the most probable explanation, the max imum aposteriori hypothesis, and the maxi mum expected utility and for updating belief are reformulated as an elimination-type al gorithm called bucket elimination. This em phasizes the principle common to many of the algorithms appearing in that literature and clarifies their relationship to nonserial dynamic programming algorithms. We also present a general way of combining condition ing and elimination within this framework.Bounds on complexity are given for all the al gorithms as a function of the problem's struc ture.