Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions

TLDR

In admissible heuristic search with consistent heuristics, all states whose f‑values are below the optimal cost—called surely expanded—must be expanded, and recent work shows that for bidirectional search, if a pair of states is surely expanded, at least one of them must be expanded. This work derives a lower bound VC on the minimum expansions needed to cover all surely expanded pairs and introduces Near‑Optimal Bidirectional Search (NBS), an admissible algorithm that guarantees no more than 2VC expansions. NBS expands nodes from both ends until all surely expanded pairs are covered, guaranteeing at most 2VC node expansions. The authors prove that no admissible front‑to‑end algorithm can achieve a worst‑case expansion count better than 2VC, and experiments demonstrate that NBS matches or surpasses existing bidirectional methods and frequently outperforms A*.

Abstract

It is well-known that any admissible unidirectional heuristic search algorithm must expand all states whose f-value is smaller than the optimal solution cost when using a consistent heuristic. Such states are called “surely expanded” (s.e.). A recent study characterized s.e. pairs of states for bidirectional search with consistent heuristics: if a pair of states is s.e. then at least one of the two states must be expanded. This paper derives a lower bound, VC, on the minimum number of expansions required to cover all s.e. pairs, and present a new admissible front-to-end bidirectional heuristic search algorithm, Near-Optimal Bidirectional Search (NBS), that is guaranteed to do no more than 2VC expansions. We further prove that no admissible front-to-end algorithm has a worst case better than 2VC. Experimental results show that NBS competes with or outperforms existing bidirectional search algorithms, and often outperforms A* as well.