Multi-Agent Path Finding on Strongly Connected Digraphs: feasibility and solution algorithms

TL;DR

This paper extends existing multi-agent pathfinding algorithms to strongly connected directed graphs, enabling efficient feasibility checks and feasible solutions in polynomial time, which is crucial for industrial applications.

Contribution

It generalizes algorithms from undirected and biconnected graphs to strongly connected directed graphs for MAPF.

Findings

Feasibility check in linear time for problems with at least two holes.

Polynomial-time algorithm for finding feasible solutions.

Extension of algorithms to a broader class of directed graphs.

Abstract

On an assigned graph, the problem of Multi-Agent Pathfinding (MAPF) consists in finding paths for multiple agents, avoiding collisions. Finding the minimum-length solution is known to be NP-hard, and computation times grows exponentially with the number of agents. However, in industrial applications, it is important to find feasible, suboptimal solutions, in a time that grows polynomially with the number of agents. Such algorithms exist for undirected and biconnected directed graphs. Our main contribution is to generalize these algorithms to the more general case of strongly connected directed graphs. In particular, given a MAPF problem with at least two holes, we present an algorithm that checks the problem feasibility in linear time with respect to the number of nodes, and provides a feasible solution in polynomial time.