# A Competitive Analysis of Online Multi-Agent Path Finding

arXiv: https://arxiv.org/abs/2106.11454 · HTML: https://mlsanity.com/paper/2106.11454/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 11 of 11)

- [Multi-Agent Pathfinding: Definitions, Variants, and Benchmarks](https://mlsanity.com/paper/1906.08291/) (2019)
- [Searching with Consistent Prioritization for Multi-Agent Path Finding](https://mlsanity.com/paper/1812.06356/) (2018)
- [Lifelong Multi-Agent Path Finding for Online Pickup and Delivery Tasks](https://mlsanity.com/paper/1705.10868/) (2017)
- [Lifelong Path Planning with Kinematic Constraints for Multi-Agent Pickup and Delivery](https://mlsanity.com/paper/1812.06355/) (2018)
- [Feasibility Study: Moving Non-Homogeneous Teams in Congested Video Game Environments](https://mlsanity.com/paper/1710.01447/) (2017)
- [MAPP: a Scalable Multi-Agent Path Planning Algorithm with Tractability and Completeness Guarantees](https://mlsanity.com/paper/1401.3905/) (2014)
- [Intractability of Optimal Multi-Robot Path Planning on Planar Graphs](https://mlsanity.com/paper/1504.02072/) (2015)
- [Idle Time Optimization for Target Assignment and Path Finding in Sortation Centers](https://mlsanity.com/paper/1912.00253/) (2019)
- [Multi-Agent Path Finding with Deadlines](https://mlsanity.com/paper/1806.04216/) (2018)
- [AI Buzzwords Explained: Multi-Agent Path Finding (MAPF)](https://mlsanity.com/paper/1710.03774/) (2017)
- [Minimizing Latency in Online Ride and Delivery Services](https://mlsanity.com/paper/1802.02744/) (2018)

## Built on by (most cited first, 2 of 2)

- [Graph-Based Multi-Robot Path Finding and Planning](https://mlsanity.com/paper/2206.11319/) (2022)
- [A General Framework for Dynamic MAPF using Multi-Shot ASP and Tunnels](https://mlsanity.com/paper/2507.20703/) (2025)

## Abstract (arXiv)

We study online Multi-Agent Path Finding (MAPF), where new agents are constantly revealed over time and all agents must find collision-free paths to their given goal locations. We generalize existing complexity results of (offline) MAPF to online MAPF. We classify online MAPF algorithms into different categories based on (1) controllability (the set of agents that they can plan paths for at each time) and (2) rationality (the quality of paths they plan) and study the relationships between them. We perform a competitive analysis for each category of online MAPF algorithms with respect to commonly-used objective functions. We show that a naive algorithm that routes newly-revealed agents one at a time in sequence achieves a competitive ratio that is asymptotically bounded from both below and above by the number of agents with respect to flowtime and makespan. We then show a counter-intuitive result that, if rerouting of previously-revealed agents is not allowed, any rational online MAPF algorithms, including ones that plan optimal paths for all newly-revealed agents, have the same asymptotic competitive ratio as the naive algorithm, even on 2D 4-neighbor grids. We also derive constant lower bounds on the competitive ratio of any rational online MAPF algorithms that allow rerouting. The results thus provide theoretical insights into the effectiveness of using MAPF algorithms in an online setting for the first time.