Exact Algorithms for Multiagent Path Finding with Communication Constraints on Tree-Like Structures

2024-12-11

AAAI Conference on Artificial Intelligence

AI Summary

This paper studies cooperative trajectory optimization for multi-agent pathfinding (MAPF) under communication connectivity constraints: agents must navigate collision-free to their goals on tree-structured or low-treewidth graphs while minimizing the makespan, subject to the requirement that the communication subgraph remains connected at all times (under bounded communication range). It introduces communication connectivity constraints formally into MAPF for the first time. Leveraging parameterized complexity theory, the authors design three fixed-parameter tractable (FPT) exact algorithms—for trees, bounded-degree graphs, and bounded-treewidth graphs—integrating tree decompositions, dynamic programming, and graph-theoretic modeling. They further prove that the problem is W[1]-hard when parameterized by the number of agents—even for makespan = 3 and communication range = 1—thereby establishing a tight computational complexity boundary.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Agent Communication
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Consider the scenario where multiple agents have to move in an optimal way through a network, each one towards their ending position, and while avoiding collisions. By optimal, we mean as fast as possible, which is evaluated by a measure known as the makespan of the proposed solution. This is the setting studied in the Multiagent Path Finding problem. In this work we additionally provide the agents with a way to communicate with each other. Due to size constraints, it is reasonable to assume that the range of the communication of each agent will be limited. What should be the trajectories of the agents to, additionally, maintain a backbone of communication? In this work we study this Multiagent Path Finding with Communication Constraint problem under the parameterized complexity framework. Our main contribution is three exact algorithms that are efficient when considering particular structures for the input network. We provide such algorithms for the case when the communication range and the number of agents (the makespan resp.) is provided in the input and the network has a tree topology, or bounded maximum degree (has a tree-like topology, i.e., bounded treewidth resp.). We complement these results by showing that it is highly unlikely to construct efficient algorithms when considering the number of agents as part of the input, even if the makespan is 3 and the communication range is 1.

Problem

• Optimal agent movement with communication constraints in networks
• Efficient exact algorithms for tree-like network structures
• Parameterized complexity analysis for multiagent path finding

Innovation

• Exact algorithms for tree-like network structures
• Communication constraints in multiagent path finding
• Parameterized complexity framework for efficiency