On the Computational Complexity of Multi-Agent Pathfinding on Directed Graphs

TL;DR

This paper investigates the computational complexity of multi-agent pathfinding on directed graphs, establishing NP-hardness in the general case and providing some upper bounds, thus clarifying the problem's difficulty.

Contribution

It proves that multi-agent pathfinding on directed graphs is NP-hard in general, resolving an open problem and extending previous polynomial-time results for special cases.

Findings

Multi-agent pathfinding on directed graphs is NP-hard.

Some upper bounds for the problem are established.

Abstract

The determination of the computational complexity of multi-agent pathfinding on directed graphs has been an open problem for many years. For undirected graphs, solvability can be decided in polynomial time, as has been shown already in the eighties. Further, recently it has been shown that a special case on directed graphs is solvable in polynomial time. In this paper, we show that the problem is NP-hard in the general case. In addition, some upper bounds are proven.