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.

翻译：多智能体路径规划在有向图上的计算复杂度确定（diMAPF）多年来一直是一个开放的研究问题。虽然diMAPF在某些特殊情况下已被证明是多项式时间可解的，但直到最近才确定该问题在一般情况下是NP难的。此外，已证明如果强连通有向图的短解假设成立，则diMAPF属于NP类。本文证明该假设确实成立，即使在允许同步旋转的情况下也是如此。