NBS is a non-parametric bidirectional search algorithm, proved to expand at most twice the number of node expansions required to verify the optimality of a solution. We introduce new variants of NBS that are aimed at finding all optimal solutions. We then introduce an algorithmic framework that includes NBS as a special case. Finally, we introduce DVCBS, a new algorithm in this framework that aims to further reduce the number of expansions. Unlike NBS, DVCBS does not have any worst-case bound guarantees, but in practice it outperforms NBS in verifying the optimality of solutions.

Recent work in bidirectional heuristic search characterize pairs of nodes from which at least one node must be expanded in order to ensure optimality of solutions. We use these findings to propose a method for improving existing heuristics by propagating lower bounds between the forward and backward frontiers. We then define a number of desirable properties for bidirectional heuristic search algorithms, and show that applying the bound propagations adds these properties to many existing algorithms (e.g. to the MM family of algorithms). Finally, experimental results show that applying these propagations significantly reduce the running time of various algorithms.

Over the past few years, there has been a great deal of theoretical and empirical work on both of these algorithms. As part of the research conducted on these algorithms, some interesting theoretical properties were proven for fMM and not for GBFSH and vice versa. In addition, both of them are used as benchmarks for evaluation bidirectional heuristic search algorithms. In this paper we show that fMM infused by a lower-bound propagation and GBFSH are equivalent. In essence, every instance of fMM can be mapped to an instance of GBFSH that expands the exact sequence of nodes and vice versa.