# Optimal Multi-Robot Path Planning on Graphs: Structure and Computational Complexity

arXiv: https://arxiv.org/abs/1507.03289 · HTML: https://mlsanity.com/paper/1507.03289/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2015.

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

- [Safe and Interpretable Multimodal Path Planning for Multi-Agent Cooperation](https://mlsanity.com/paper/2602.19304/) (2026)

## Abstract (arXiv)

We study the problem of optimal multi-robot path planning on graphs (MPP) over four distinct minimization objectives: the total arrival time, the makespan (last arrival time), the total distance, and the maximum (single-robot traveled) distance. On the structure side, we show that each pair of these four objectives induces a Pareto front and cannot always be optimized simultaneously. Then, through reductions from 3-SAT, we further establish that computation over each objective is an NP-hard task, providing evidence that solving MPP optimally is generally intractable. Nevertheless, in a related paper, we design complete algorithms and efficient heuristics for optimizing all four objectives, capable of solving MPP optimally or near-optimally for hundreds of robots in challenging setups.