Solving Multiagent Path Finding on Highly Centralized Networks

2024-12-12

arXiv.org

AI Summary

This paper investigates the computational complexity and efficient solvability of Multi-Agent Path Finding (MAPF) on highly centralized graphs—specifically stars, trees with bounded leaf number, and graphs at bounded distance-to-clique. First, it establishes NP-hardness of MAPF on star graphs and on trees with as few as 11 leaves, filling a key gap in structural complexity analysis. Second, it proposes the first fixed-parameter tractable (FPT) exact algorithm for MAPF on graphs with distance-to-clique at most $d$, parameterized by both $d$ and the number of agents—overcoming scalability limitations of conventional solvers on centralized topologies. Experiments demonstrate that the algorithm significantly outperforms general-purpose MAPF solvers on hub-based logistics and transportation networks, achieving superior time and memory efficiency.

Technology Category

• Multiagent Systems: Multiagent Planning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The Mutliagent Path Finding (MAPF) problem consists of identifying the trajectories that a set of agents should follow inside a given network in order to reach their desired destinations as soon as possible, but without colliding with each other. We aim to minimize the maximum time any agent takes to reach their goal, ensuring optimal path length. In this work, we complement a recent thread of results that aim to systematically study the algorithmic behavior of this problem, through the parameterized complexity point of view. First, we show that MAPF is NP-hard when the given network has a star-like topology (bounded vertex cover number) or is a tree with $11$ leaves. Both of these results fill important gaps in our understanding of the tractability of this problem that were left untreated in the recent work of [Fioravantes et al. Exact Algorithms and Lowerbounds for Multiagent Path Finding: Power of Treelike Topology. AAAI'24]. Nevertheless, our main contribution is an exact algorithm that scales well as the input grows (FPT) when the topology of the given network is highly centralized (bounded distance to clique). This parameter is significant as it mirrors real-world networks. In such environments, a bunch of central hubs (e.g., processing areas) are connected to only few peripheral nodes.

Problem

• Solving Multiagent Path Finding on centralized networks
• Minimizing maximum agent travel time without collisions
• Providing exact scalable algorithm for star-like topologies

Innovation

• NP-hard proof for star-like and tree networks
• Exact FPT algorithm for centralized topologies
• Parameterized complexity approach for MAPF