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.

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*.

In a multi-agent path-finding (MAPF) problem, the task is to find a plan for moving a set of agents from their initial locations to their goals without collisions. Following this plan, however, may not be possible due to unexpected events that delay some of the agents. Guaranteeing that collisions will never occur may be impossible. An important task is to find a plan that is very likely to succeed, even though unexpected delays may occur. We propose an algorithm for finding a plan in which the probability that no collisions will occur is at least a given parameter p (p-robust plan). We show that finding an optimal p-robust plan is significantly more difficult than finding an optimal standard plan. As a practical solution, we propose a greedy algorithm based on the Conflict-Based Search framework. Our experiments show that it finds p-robust plans with cost that is relatively close to the optimal cost of the standard, non-robust plans.

The MAPF problem is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses and autonomous vehicles. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers make different assumptions, e.g., whether agents can traverse the same road at the same time, and have different objective functions, e.g., minimize makespan or sum of agents' actions costs. These assumptions and objectives are sometimes implicitly assumed or described informally. This makes it difficult to establish appropriate baselines for comparison in research papers, as well as making it difficult for practitioners to find the papers relevant to their concrete application. This paper aims to fill this gap and support researchers and practitioners by providing a unifying terminology for describing common MAPF assumptions and objectives. In addition, we also provide pointers to two MAPF benchmarks. In particular, we introduce a new grid-based benchmark for MAPF, and demonstrate experimentally that it poses a challenge to contemporary MAPF algorithms.

MAPF is the problem of finding paths for multiple agents such that every agent reaches its goal and the agents do not collide. Most prior work on MAPF were on grid, assumed all actions cost the same, agents do not have a volume, and considered discrete time steps. In this work we propose a MAPF algorithm that do not assume any of these assumptions, is complete, and provides provably optimal solutions. This algorithm is based on a novel combination of SIPP, a continuous time single agent planning algorithms, and CBS, a state of the art multi-agent pathfinding algorithm. We analyze this algorithm, discuss its pros and cons, and evaluate it experimentally on several standard benchmarks.