Constrained Multi-Agent Path Finding on Directed Graphs

TL;DR

This paper introduces constrained multi-agent pathfinding on directed graphs, incorporating safety distance constraints, proves NP-hardness, and proposes a reduction method to standard problems.

Contribution

It extends classical MP and MAPF problems with new vertex subset constraints and provides a reduction approach to solve them.

Findings

C-MP and C-MAPF are NP-hard to solve.

A reduction method to standard MP and MAPF is proposed.

Finding maximum cardinality subset W is strongly NP-hard.

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.