In this paper we study bidirectional state space search with consistent heuristics, with a focus on obtaining sufficient conditions for node expansion, that is, conditions characterizing nodes that must be expanded by any admissible bidirectional search algorithm. We provide such conditions for front-to-front and front-to-end bidirectional search. The sufficient conditions are used to prove that the front-to-front bidirectional search algorithm BDS1 is optimally efficient, in terms of node expansion, among a broad class of bidirectional search algorithms, for a specific class of problem instances. Dechter and Pearl's well-known result on sufficient conditions for node expansion by unidirectional algorithms such as A* is shown to be a special case of our results.
We thank Ariel Felner and the anonymous reviewers for many suggestions that improved the paper. Financial support for this research was in part provided by Canada’s Natural Sciences and Engineering Research Council (NSERC). This material is based upon work supported by the National Science Foundation under Grant No. 1551406.
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