The Small Solution Hypothesis for MAPF on Strongly Connected Directed Graphs Is True

TL;DR

This paper proves the Small Solution Hypothesis for multi-agent pathfinding on strongly connected directed graphs, confirming that solutions can be small even with synchronous rotations, which impacts the understanding of the problem's complexity.

Contribution

It establishes the truth of the Small Solution Hypothesis for strongly connected directed graphs in diMAPF, including cases with synchronous rotations.

Findings

The hypothesis holds true for strongly connected directed graphs.

Solutions can be small even with synchronous rotations.

Implications for the complexity classification of diMAPF.

Abstract

The determination of the computational complexity of multi-agent pathfinding on directed graphs (diMAPF) has been an open research problem for many years. While diMAPF has been shown to be polynomial for some special cases, only recently, it has been established that the problem is NP-hard in general. Further, it has been proved that diMAPF will be in NP if the short solution hypothesis for strongly connected directed graphs is correct. In this paper, it is shown that this hypothesis is indeed true, even when one allows for synchronous rotations.