Distance-Constrained Unlabeled Multi-Agent Pathfinding

2026-05-12

AI Summary

This study addresses the unlabeled multi-agent path planning problem under distance constraints, where agents must maintain a pairwise separation of at least $r+1$ at all times to avoid collisions and satisfy coordination requirements. The work establishes, for the first time, that this problem is PSPACE-complete. To tackle its computational hardness, the authors propose a hybrid solving framework: on one hand, they achieve theoretically optimal solutions through problem reduction and feasibility-preserving compression; on the other, they introduce a configuration-based search strategy to enhance scalability. Experimental results demonstrate that the proposed approach efficiently handles large-scale instances with hundreds of agents within reasonable timeframes, significantly outperforming existing methods.

Abstract

We study a graph pathfinding problem Distance-$r$ Independent Unlabeled Multi-Agent Pathfinding, finding a set of collision-free paths between two sets where agents must stay at pairwise distance at least $r+1$ at all times. This additional constraint, generalizing collision modeling for classical MAPF, targets aspects of real-world multi-agent coordination. This additional distance constraint makes feasibility (i.e., whether a solution exists) PSPACE-complete, in contrast to standard (unlabeled) MAPF, where it can be decided in polynomial time. We address the challenge via two complementary approaches: (i) reduction-based optimal algorithms with a feasibility-preserving compression procedure, and (ii) a configuration generator-based search. Despite the hardness, empirical results show that our algorithm can handle hundreds of agents in a practical timeframe.

Problem

• Multi-Agent Pathfinding
• Distance Constraint
• Collision-Free Paths
• Unlabeled Agents
• PSPACE-Completeness

Innovation

• Distance-constrained MAPF
• Unlabeled Multi-Agent Pathfinding
• PSPACE-completeness
• Feasibility-preserving compression
• Configuration generator