English

Constrained Multi-Agent Path Finding on Directed Graphs

Multiagent Systems 2024-04-10 v1

Abstract

We discuss C-MP and C-MAPF, generalizations of the classical Motion Planning (MP) and Multi-Agent Path Finding (MAPF) problems on a directed graph G. Namely, we enforce an upper bound on the number of agents that occupy each member of a family of vertex subsets. For instance, this constraint allows maintaining a safety distance between agents. We prove that finding a feasible solution of C-MP and C-MAPF is NP-hard, and we propose a reduction method to convert them to standard MP and MAPF. This reduction method consists in finding a subset of nodes W and a reduced graph G/W, such that a solution of MAPF on G/W provides a solution of C-MAPF on G. Moreover, we study the problem of finding W of maximum cardinality, which is strongly NP-hard.

Keywords

Cite

@article{arxiv.2209.12506,
  title  = {Constrained Multi-Agent Path Finding on Directed Graphs},
  author = {Stefano Ardizzoni and Luca Consolini and Marco Locatelli and Irene Saccani},
  journal= {arXiv preprint arXiv:2209.12506},
  year   = {2024}
}