# Optimal Target Assignment and Path Finding for Teams of Agents

arXiv: https://arxiv.org/abs/1612.05693 · HTML: https://mlsanity.com/paper/1612.05693/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2016.

## Built on by (most cited first, 25 of 25)

- [Answer Set Planning: A Survey](https://mlsanity.com/paper/2202.05793/) (2022)
- [Decentralized Monte Carlo Tree Search for Partially Observable Multi-agent Pathfinding](https://mlsanity.com/paper/2312.15908/) (2023)
- [MS*: A New Exact Algorithm for Multi-agent Simultaneous Multi-goal Sequencing and Path Finding](https://mlsanity.com/paper/2103.09979/) (2021)
- [Cooperative Multi-Agent Path Finding: Beyond Path Planning and Collision Avoidance](https://mlsanity.com/paper/2105.10993/) (2021)
- [Graph-Based Multi-Robot Path Finding and Planning](https://mlsanity.com/paper/2206.11319/) (2022)
- [Optimal and Bounded-Suboptimal Multi-Goal Task Assignment and Path Finding](https://mlsanity.com/paper/2208.01222/) (2022)
- [A Conflict-Based Search Framework for Multi-Objective Multi-Agent Path Finding](https://mlsanity.com/paper/2101.03805/) (2021)
- [Improved Anonymous Multi-Agent Path Finding Algorithm](https://mlsanity.com/paper/2312.10572/) (2023)
- [Solving Multi-Agent Target Assignment and Path Finding with a Single Constraint Tree](https://mlsanity.com/paper/2307.00663/) (2023)
- [Safe and Interpretable Multimodal Path Planning for Multi-Agent Cooperation](https://mlsanity.com/paper/2602.19304/) (2026)
- [Simultaneous Task Allocation and Planning for Multi-Robots under Hierarchical Temporal Logic Specifications](https://mlsanity.com/paper/2401.04003/) (2024)
- [Symbolic Planning and Multi-Agent Path Finding in Extremely Dense Environments with Unassigned Agents](https://mlsanity.com/paper/2509.01022/) (2025)
- [Multi-objective Conflict-based Search Using Safe-interval Path Planning](https://mlsanity.com/paper/2108.00745/) (2021)
- [Fairness in Multi-Agent Planning](https://mlsanity.com/paper/2212.00506/) (2022)
- [Fine-Grained Complexity Analysis of Multi-Agent Path Finding on 2D Grids](https://mlsanity.com/paper/2305.16303/) (2023)
- [ITA-ECBS: A Bounded-Suboptimal Algorithm for the Combined Target-Assignment and Path-Finding Problem](https://mlsanity.com/paper/2404.05223/) (2024)
- [DMS*: Minimizing Makespan for Multi-Agent Combinatorial Path Finding](https://mlsanity.com/paper/2312.06314/) (2023)
- [Optimal Task Assignment and Path Planning using Conflict-Based Search with Precedence and Temporal Constraints](https://mlsanity.com/paper/2402.08772/) (2024)
- [A Conflict-Aware Optimal Goal Assignment Algorithm for Multi-Robot Systems](https://mlsanity.com/paper/2402.13292/) (2024)
- [Optimal Integrated Task and Path Planning and Its Application to Multi-Robot Pickup and Delivery](https://mlsanity.com/paper/2403.01277/) (2024)
- [Multi-robot Path Planning and Scheduling via Model Predictive Optimal Transport (MPC-OT)](https://mlsanity.com/paper/2508.21205/) (2025)
- [Solving Multi-Agent Multi-Goal Path Finding Problems in Polynomial Time](https://mlsanity.com/paper/2512.22171/) (2025)
- [Alternating Target-Path Planning for Scalable Multi-Agent Coordination](https://mlsanity.com/paper/2605.07744/) (2026)
- [Optimal and Scalable MAPF via Multi-Marginal Optimal Transport and Schr"odinger Bridges](https://mlsanity.com/paper/2605.10917/) (2026)
- [Pivot-and-Station Multi-Agent Path Finding: Solvability, Complexity, and Algorithms](https://mlsanity.com/paper/2608.24585/) (2026)

## Abstract (arXiv)

We study the TAPF (combined target-assignment and path-finding) problem for teams of agents in known terrain, which generalizes both the anonymous and non-anonymous multi-agent path-finding problems. Each of the teams is given the same number of targets as there are agents in the team. Each agent has to move to exactly one target given to its team such that all targets are visited. The TAPF problem is to first assign agents to targets and then plan collision-free paths for the agents to their targets in a way such that the makespan is minimized. We present the CBM (Conflict-Based Min-Cost-Flow) algorithm, a hierarchical algorithm that solves TAPF instances optimally by combining ideas from anonymous and non-anonymous multi-agent path-finding algorithms. On the low level, CBM uses a min-cost max-flow algorithm on a time-expanded network to assign all agents in a single team to targets and plan their paths. On the high level, CBM uses conflict-based search to resolve collisions among agents in different teams. Theoretically, we prove that CBM is correct, complete and optimal. Experimentally, we show the scalability of CBM to TAPF instances with dozens of teams and hundreds of agents and adapt it to a simulated warehouse system.