Abstract
Two models of heuristics have been suggested in previous studies of A* tree-searching. The models are used to determine what mathematical properties heuristics must have if A* is to have polynomial, versus exponential, average asymptotic time complexity. In the EC model polynomial A* complexity is associated with logarithmic heuristic error. In the NC model it is associated with a concentration ofh-values near a rapidly growing central function; logarithmic clustering is adequate but more deviation is allowed if the central function grows fast enough.
This paper introduces a third model based on approximating heuristic values with normally distributed random variables — the ND model. The ND model predicts polynomial A* complexity when the mean ofh-values is rapidly growing and variance is logarithmic. The three models are compared. They are tested by attempting to explain the success of weighting heuristics to reduce A* complexity. The EC model is found inadequate; the NC and ND models reveal situations in which weighting changes time complexity from exponential to polynomial. These results are largely corroborated by statistical data from a particular problem domain.
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This research has been partially funded by a grant from NCR Corporation.
This research has been funded by NCR Corporation.
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Davis, H.W., Chenoweth, S.V. The mathematical modeling of heuristics. Ann Math Artif Intell 5, 191–227 (1992). https://doi.org/10.1007/BF01543476
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DOI: https://doi.org/10.1007/BF01543476