Distance-Constrained Unlabeled Multi-Agent Pathfinding

TL;DR

This paper introduces a new multi-agent pathfinding problem with distance constraints, showing its computational complexity and proposing algorithms that perform well in practice.

Contribution

It formalizes the distance-constrained unlabeled MAPF problem, proves its PSPACE-completeness, and develops algorithms that efficiently handle large instances empirically.

Findings

Feasibility is PSPACE-complete with distance constraints.

Algorithms can handle hundreds of agents practically.

Proposed methods outperform baseline approaches in experiments.

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.