PSPACE-Completeness of Multi-Agent Path Finding for Large Agents

Maichi Zhang; Naoyuki Kamiyama; Kanae Yoshiwatari

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arXiv · 2608.12955

PSPACE-Completeness of Multi-Agent Path Finding for Large Agents

Maichi Zhang·Naoyuki Kamiyama·Kanae Yoshiwatari

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Abstract

Multi-Agent Path Finding for Large Agents (LA-MAPF) is a geometric variant of MAPF in which agents are modeled as disks and conflicts are determined by physical overlap in the underlying Euclidean workspace. The goal of LA-MAPF is to decide whether there exists a sequence of conflict-free transitions from a start configuration to a goal configuration. Agafonov and Yakovlev proved that LA-MAPF is NP-hard. In this paper, we strengthen their result by proving that LA-MAPF is PSPACE-complete via a polynomial-time reduction from Restricted Sliding Tokens.

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Maichi Zhang, Naoyuki Kamiyama, Kanae Yoshiwatari. 2026-08-13. PSPACE-Completeness of Multi-Agent Path Finding for Large Agents. https://arxiv.org/abs/2608.12955

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