Polynomial-time Configuration Generator for Connected Unlabeled Multi-Agent Pathfinding

2025-10-22

AI Summary

This paper addresses the Connected Unlabeled Multi-Agent Path Finding (CUMAPF) problem, which requires maintaining persistent connectivity of a mobile agent swarm during navigation to support collective robotic tasks such as self-reconfiguration and coordinated locomotion. As an NP-hard problem on constrained graphs, CUMAPF suffers from computational bottlenecks in existing approaches. We propose PULL—the first algorithmic framework that is both complete and polynomial-time bounded (O(n²) per step). Its core is a rule-based single-step state transition mechanism that jointly enforces connectivity preservation and goal-directed progress, and it is designed to integrate seamlessly with search-based MAPF solvers. Experiments demonstrate that PULL scales efficiently to hundreds of agents, yields significantly higher-quality solutions than naive strategies, and guarantees optimality for small-scale instances.

Technology Category

• Multiagent Systems: Multiagent Planning
• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

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

Abstract

We consider Connected Unlabeled Multi-Agent Pathfinding (CUMAPF), a variant of MAPF where the agents must maintain connectivity at all times. This problem is fundamental to swarm robotics applications like self-reconfiguration and marching, where standard MAPF is insufficient as it does not guarantee the required connectivity between agents. While unlabeled MAPF is tractable in optimization, CUMAPF is NP-hard even on highly restricted graph classes. To tackle this challenge, we propose PULL, a complete and polynomial-time algorithm with a simple design. It is based on a rule-based one-step function that computes a subsequent configuration that preserves connectivity and advances towards the target configuration. PULL is lightweight, and runs in $O(n^2)$ time per step in 2D grid, where $n$ is the number of agents. Our experiments further demonstrate its practical performance: PULL finds competitive solution qualities against trivial solutions for hundreds of agents, in randomly generated instances. Furthermore, we develop an eventually optimal solver that integrates PULL into an existing search-based MAPF algorithm, providing a valuable tool for small-scale instances.

Problem

• Maintaining agent connectivity in multi-agent pathfinding
• Solving NP-hard connected unlabeled MAPF efficiently
• Providing polynomial-time algorithm for swarm robotics applications

Innovation

• Polynomial-time algorithm for connected multi-agent pathfinding
• Rule-based one-step function preserving agent connectivity
• Lightweight O(n^2) per-step computation in 2D grids