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

arXiv: https://arxiv.org/abs/2209.04286 · HTML: https://mlsanity.com/paper/2209.04286/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2022.

## Built on by (most cited first, 1 of 1)

- [The Small Solution Hypothesis for MAPF on Strongly Connected Directed Graphs Is True](https://mlsanity.com/paper/2210.04590/) (2022)

## Abstract (arXiv)

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.