Empirical Hardness in Multi-Agent Pathfinding: Research Challenges and Opportunities

TL;DR

This paper explores the variability in solving multi-agent pathfinding problems, identifying key challenges in understanding empirical hardness, and proposing directions for future research to improve algorithm selection and benchmark generation.

Contribution

It highlights the gap between theoretical complexity and practical hardness in MAPF, and outlines three research challenges to better understand and leverage empirical hardness.

Findings

Empirical hardness varies significantly across MAPF instances.

Understanding instance features can improve algorithm selection.

Generating diverse hard instances can enhance benchmarking.

Abstract

Multi-agent pathfinding (MAPF) is the problem of finding collision-free paths for a team of agents on a map. Although MAPF is NP-hard, the hardness of solving individual instances varies significantly, revealing a gap between theoretical complexity and actual hardness. This paper outlines three key research challenges in MAPF empirical hardness to understand such phenomena. The first challenge, known as algorithm selection, is determining the best-performing algorithms for a given instance. The second challenge is understanding the key instance features that affect MAPF empirical hardness, such as structural properties like phase transition and backbone/backdoor. The third challenge is how to leverage our knowledge of MAPF empirical hardness to effectively generate hard MAPF instances or diverse benchmark datasets. This work establishes a foundation for future empirical hardness research and encourages deeper investigation into these promising and underexplored areas.