Bidirectional Heuristic Search Reconsidered

Abstract

The assessment of bidirectional heuristic search has been incorrect since it was rst published more than a quarter of a century ago. For quite a long time, this search strategy did not achieve the expected results, and there was a major misunderstanding about the reasons behind it. Although there is still wide-spread belief that bidirectional heuristic search is a icted by the problem of search frontiers passing each other, we demonstrate that this conjecture is wrong. Based on this nding, we present both a new generic approach to bidirectional heuristic search and a new approach to dynamically improving heuristic values that is feasible in bidirectional search only. These approaches are put into perspective with both the traditional and more recently proposed approaches in order to facilitate a better overall understanding. Empirical results of experiments with our new approaches show that bidirectional heuristic search can be performed very e ciently and also with limited memory. These results suggest that bidirectional heuristic search appears to be better for solving certain di cult problems than corresponding unidirectional search. This provides some evidence for the usefulness of a search strategy that was long neglected. In summary, w e show that bidirectional heuristic search is viable and consequently propose that it be reconsidered. Background and IntroductionWhen a problem is represented as a state space graph, solutions to such a problem are paths from a given start node s to some goal target node t. Finding such a solution can be attempted by searching this graph. If the search is guided by heuristic information, it is called a heuristic search. Most of the work on heuristic search for problem solving deals with unidirectional approaches, that start from s heading towards some node t see, e.g., Pearl, 1984. When there is one goal node t explicitly given and the search operators are reversible, bidirectional search is possible, which proceeds both in the forward direction from s to t and in the backward direction from t to s see, e.g., Nilsson, 1980. Strictly speaking, it is not even required that operators have i n verses. It is just necessary that for a given node n the set of parent nodes p i can be determined for which there exist operators that lead from p i to n. Searching backwards means generating parent nodes successively from the goal node t see, e.g., Russell & Norvig, 1995. In other words, backward search implements reasoning about the operators in the backward direction.As an illustrating example of a class of problems where bidirectional search can be usefully applied, consider nding nd a shortest path between two given places s and t using a given map of some city. In case of one-way streets, bidirectional search implements

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