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.

While the study of unit-cost Multi-Agent Pathfinding (MAPF) problems has been popular, many real-world problems require continuous time and costs due to various movement models. In this context, this paper studies symmetry-breaking enhancements for Continuous-Time Conflict-Based Search (CCBS), a solver for continuous-time MAPF. Resolving conflict symmetries in MAPF can require an exponential amount of work. We adapt known enhancements from unit-cost domains for CCBS: bypassing, which resolves cost symmetries and biclique constraints which resolve spatial conflict symmetries. We formulate a novel combination of biclique constraints with disjoint splitting for spatial conflict symmetries. Finally, we show empirically that these enhancements yield a statistically significant performance improvement versus previous state of the art, solving problems for up to 10% or 20% more agents in the same amount of time on dense graphs.

The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking these factors into consideration can potentially lead to a performance boost in relevant applications. Recently, a generalized framework for weighted directed graphs was suggested, where edge-weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. We build on this framework to introduce the problem of finding the tightest admissible shortest path (TASP); a path with the tightest suboptimality bound on the optimal cost. This is a generalization of the shortest path problem to bounded uncertainty, where edge-weight uncertainty can be traded for computational cost. We present a complete algorithm for solving TASP, with guarantees on solution quality. Empirical evaluation supports the effectiveness of this approach.

The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. This raises several generalized variants of the shortest path problem. We introduce the problem of finding a path with the tightest lower-bound on the optimal cost. We then present two complete algorithms for the generalized problem, and empirically demonstrate their efficacy.

This paper solves the Watchman Route Problem (WRP) on a general discrete graph with Heuristic Search. Given a graph, a line-of-sight (LOS) function, and a start vertex, the task is to (offline) find a (shortest) path through the graph such that all vertices in the graph will be visually seen by at least one vertex on the path. WRP is reminiscent but different from graph covering and mapping problems, which are done online on an unknown graph. We formalize WRP as a heuristic search problem and solve it optimally with an A*-based algorithm. We develop a series of admissible heuristics with increasing difficulty and accuracy. Our heuristics abstract the underlying graph into a disjoint line-of-sight graph (GDLS) which is based on disjoint clusters of vertices such that vertices within the same cluster have LOS to the same specific vertex. We use solutions for the Minimum Spanning Tree (MST) and the Traveling Salesman Problem (TSP) of GDLS as admissible heuristics for WRP. We theoretically and empirically investigate these heuristics. Then, we show how the optimal methods can be modified (by intelligently pruning away large sub-trees) to obtain various suboptimal solvers with and without bound guarantees. These suboptimal solvers are much faster and expand fewer nodes than the optimal solver with only minor reduction in the quality of the solution.

In this paper, we formalize and study the Moving Agents in Formation (MAiF) problem, that combines the tasks of finding short collision-free paths for multiple agents and keeping them in close adherence to a desired formation. Previous work includes controller-based algorithms, swarm-based algorithms, and potential-field-based algorithms. They usually focus on only one or the other of these tasks, solve the problem greedily without systematic search, and thus generate costly solutions or even fail to find solutions in congested environment. In this paper, we develop a two-phase search algorithm, called SWARM-MAPF, whose first phase is inspired by swarm-based algorithms (in open regions) and whose second phase is inspired by multi-agent path-finding (MAPF) algorithms (in congested regions). In the first phase, SWARM-MAPF selects a leader among the agents and finds a path for it that is sufficiently far away from the obstacles so that the other agents can preserve the desired formation around it. It also identifies the critical segments of the leader's path where the other agents cannot preserve the desired formation and the refinement of which has thus to be delegated to the second phase. In the second phase, SWARM-MAPF refines these segments. Theoretically, we prove that SWARM-MAPF is complete. Empirically, we show that SWARM-MAPF scales well and is able to find close-to-optimal solutions.

In this paper we optimally solve the Watchman Route Problem (WRP) on a grid. We are given a grid map with obstacles and the task is to (offline) find a (shortest) path through the grid such that all cells in the map can be visually seen by at least one c ll on the path. WRP is a reminiscent but is different from graph covering and mapping problems which are done online on an unknown graph. We formalize WRP as a heuristic search problem and solve it with an A*-based algorithm. We develop a series of admissible heuristics with increasing difficulty and accuracy. In particular, our heuristics abstract the problem into line-of-sight clusters graph. Then, solutions for the minimum spanning tree (MST) and the traveling salesman problem (TSP) on this graph are used as admissible heuristics for WRP. We theoretically and experimentally study these heuristics and show that we can optimally and suboptimally solve problems of increasing difficulties.

Multi-Agent Path Finding (MAPF) is the problem of finding non-colliding paths for multiple agents. The classical problem assumes that all agents are homogeneous, with a fixed size and behavior. However, in reality agents are heterogeneous, with different sizes and behaviors. In this paper, we generalize MAPF to G-MAPF for the case of heterogeneous agents. We then show how two previous settings of large agents and k-robust agents are special cases of G-MAPF. Finally, we introduce G-CBS, a variant of the Conflict-Based Search (CBS) algorithm for G-MAPF, which does not cause significant extra overhead.

In the Multi-Agent Meeting (MAM) problem, the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a Multi-Directional Search algorithm that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding optimal meeting locations for multiple agents. A number of admissible heuristics are proposed and experiments demonstrate the benefits of MM*.

fMM and GBFSH are two prominent bidirectional heuristic search 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. This equivalence indicates that all theoretical properties proven for one algorithm hold for both algorithm, and that future analyses and benchmarks can consider only one of these algorithms.