Map Connectivity and Empirical Hardness of Grid-based Multi-Agent Pathfinding Problem

Jingyao Ren, Eric Ewing, T. K. Satish Kumar, Sven Koenig, Nora Ayanian

Keywords: Multi-Agent Path Planning, Empirical Hardness

TL;DR: An empirical study on the relationship between map connectivity and the empirical hardness of multi-agent pathfinding (MAPF) problem

Abstract: We present an empirical study of the relationship between map connectivity and the empirical hardness of the multi-agent pathfinding~(MAPF) problem. By analyzing the second smallest eigenvalue~(commonly known as $\lambda_2$) of the normalized Laplacian matrix of different maps, our initial study indicates that maps with smaller $\lambda_2$ tend to create more challenging instances when agents are generated uniformly randomly. Additionally, we introduce a map generator based on Quality Diversity~(QD) that is capable of producing maps with specified $\lambda_2$ ranges, offering a possible way for generating challenging MAPF instances. Despite the absence of a strict monotonic correlation with $\lambda_2$ and the empirical hardness of MAPF, this study serves as a valuable initial investigation for gaining a deeper understanding of what makes a MAPF instance hard to solve.

Primary Keywords: Multi-Agent Planning

Category: Short

Student: Graduate

Submission Number: 139