Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions
This work addresses the efficiency of search algorithms for pathfinding problems, providing a near-optimal solution with proven bounds, though it is incremental as it builds on prior bidirectional search research.
The paper tackled the problem of minimizing node expansions in bidirectional heuristic search by deriving a lower bound VC and presenting the Near-Optimal Bidirectional Search (NBS) algorithm, which guarantees no more than 2VC expansions and often outperforms existing algorithms including A* in experiments.
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.