Parallelization and External Memory (PEM) techniques have significantly enhanced the capabilities of search algorithms when solving large-scale problems. Previous research on PEM has primarily centered on unidirectional algorithms, with only one publication on bidirectional PEM that focuses on the meet-in-the-middle (MM) algorithm. Building upon this foundation, this paper presents a framework that integrates both uni- and bi-directional best-first search algorithms into this framework. We then develop a PEM variant of the state-of-the-art bidirectional heuristic search (BiHS) algorithm BAE* (PEM-BAE*). As previous work on BiHS did not focus on scaling problem sizes, this work enables us to evaluate bidirectional algorithms on hard problems. Empirical evaluation shows that PEM-BAE* outperforms the PEM variants of A* and the MM algorithm, as well as a parallel variant of IDA*. These findings mark a significant milestone, revealing that bidirectional search algorithms clearly outperform unidirectional search algorithms across several domains, even when equipped with state-of-the-art heuristics.

This paper introduces Bidirectional Guidance Informed Trees (BIGIT*),~a new asymptotically optimal sampling-based motion planning algorithm. Capitalizing on the strengths of \emph{meet-in-the-middle} property in bidirectional heuristic search with a new lazy strategy, and uniform-cost search, BIGIT* constructs an implicitly bidirectional preliminary motion tree on an implicit random geometric graph (RGG). This efficiently tightens the informed search region, serving as an admissible and accurate bidirectional guidance heuristic. This heuristic is subsequently utilized to guide a bidirectional heuristic search in finding a valid path on the given RGG. Experiments show that BIGIT* outperforms the existing informed sampling-based motion planners both in faster finding an initial solution and converging to the optimum on simulated abstract problems in $\mathbb{R}^{16}$. Practical drone flight path planning tasks across a campus also verify our results.

This paper proves several new properties of the Meet in the Middle (MMe) bidirectional heuristic search algorithm when applied to graphs with unit edge costs. Primarily, it is shown that the length of the first path discovered by MMe never exceeds the optimal length by more than one and that if the length of the first path found is odd, then it must be optimal. These properties suggest that the search strategy should emphasize finding a complete path as soon as possible. Computational experiments demonstrate that fully exploiting these new properties can decrease the number of nodes expanded by anywhere from twofold to over tenfold.

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.

The state of the art in bidirectional search has changed significantly a very short time period; we now can answer questions about unidirectional and bidirectional search that until very recently we were unable to answer. This paper is designed to provide an accessible overview of the recent research in bidirectional search in the context of the broader efforts over the last 50 years. We give particular attention to new theoretical results and the algorithms they inspire for optimal and near-optimal node expansions when finding a shortest path.

Bidirectional search algorithms interleave a search forward from the start state (start ) and a search backward (i.e. using reverse operators) from the goal state (goal). We say that the two searches “meet in the middle” if neither search expands a node whose g-value (in the given direction) exceeds C*/2 , where C* is the cost of an optimal solution. The only bidirectional heuristic search algorithm that is guaranteed to meet in the middle under all circumstances is the recently introduced MM algorithm (Holte et al. 2016). The feature of MM that provides this guarantee is its unique priority functions for nodes on its open lists. In this short note we present MMe, which enhances MM’s priority function and is expected to expand fewer nodes than MM under most circumstances. We sketch a proof of MMe’s correctness, describe conditions under which MMe will expand fewer nodes than MM and vice versa, and experimentally compare MMe and MM on the 10-Pancake problem.

We present an intuitive explanation for the limited effectiveness of front-to-end bidirectional heuristic search, supported with extensive evidence from many commonly-studied domains. While previous work has proved the limitations of specific algorithms, we show that any front-to-end bidirectional heuristic search algorithm will likely be dominated by unidirectional heuristic search or bidirectional brute-force search. We also demonstrate a pathological case where bidirectional heuristic search is the dominant algorithm, so a stronger claim cannot be made. Finally, we show that on the four-peg Towers Of Hanoi with arbitrary start and goal states, bidirectional brute-force search outperforms unidirectional heuristic search using pattern-database heuristics.