A parallelizable variant of HCA*

TL;DR

The paper tackles multi-agent path finding (MAPF) on $M\times M$ grids with $N$ homogeneous agents, addressing scalability of HCA* by introducing a parallelizable variant. In each iteration, agents compute shortest paths, an intersection graph (IG) is formed to identify colliding paths, and an approximate maximum independent set (MIS) is used to fix a subset of agent paths while the remaining agents replan via space-time A* (Reverse Resumable A*). Parallelism is achieved both at the level of independent path computations and IG construction through map partitioning, with an efficient path-encoding and communication scheme. Simulations across multiple maps show cost reductions in many cases and speedups up to about $4\times$ compared with HCA*, indicating practical scalability benefits for MAPF in large-scale or real-time settings. The approach also opens avenues for integration with WHCA* in future work and highlights the importance of partitioned parallel computation and communication considerations in distributed MAPF planning.

Abstract

This paper presents a parallelizable variant of the well-known Hierarchical Cooperative A* algorithm (HCA*) for the multi-agent path finding (MAPF) problem. In this variant, all agents initially find their shortest paths disregarding the presence of others. This is done using A*. Then an intersection graph (IG) is constructed; each agent is a node and two nodes have an edge between them if the paths of corresponding agents collide. Thereafter, an independent set is extracted with the aid of an approximation algorithm for the maximum independent set problem. The paths for the agents belonging to independent set are fixed. The rest of agents now again find their shortest paths, this time ensuring no collision with the prior agents. Space-time A*, which is a crucial component of HCA*, is used here. These iterations continue until no agents are left. Since the tasks of finding shortest paths for the agents in any iteration are independent of each other, the proposed algorithm can be parallelized to a large extent. In addition to this, the task of determining the IG can also be done in parallel by dividing the map into sections and with each agent focusing on a particular section. The parallelism does come at a cost of communication between the agents and the server. This is accounted for in the simulations. As an added advantage, the user need not make a choice for the priority order. It is observed, empirically, that the proposed algorithm outperforms HCA* in terms of the computation time and the cost value in many cases. Simulations are provided for corroboration.

Figures (6)

• Figure 1: A typical problem configuration for the MAPF problem. This image shows the Berlin Map stern2019mapf with source and goal locations for 5 agents marked by $S_1, S_2, S_3, S_4, S_5$ and $G_1, G_2, G_3, G_4, G_5$, respectively. The task is to find non-colliding paths for the 5 agents such that the sum of their path lengths (including waiting times) is minimum. This map is also used for benchmarking.
• Figure 2: A pseudocode of the instance generation routine shown above generates a problem instance ensuring that prioritized path planning yields a solution under any priority order.
• Figure 3: A pseudo-code of the proposed variant of HCA* in this paper.
• Figure 4: An example showing the working of the proposed method for an instance with 4 agents on $12\times 12$ grid. The grid has no obstacles for the sake of simplicity. There are four agents marked using four different colors. The starting nodes are the ones where the paths begin, and the ending nodes are the ends with small circles. It can be seen that there are two collisions in the first step, shown by stars. The IG is shown, from which an independent set is extracted (shown by encircled red and green nodes). The agents corresponding to the other nodes (blue and orange) are recomputed. The final result in shown in the image on the RHS.
• Figure 5: A schematic showing the four partitions of the map, each colored with a different color. Here each color represents the agent to which the partition is allocated. Note that the path partitions can be found out by determining the segments of paths that lie within each partition.