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

2025-12-10

AI Summary

Although Multi-Agent Path Finding (MAPF) is NP-hard, empirical hardness varies significantly across instances, revealing a gap between theoretical complexity and practical solvability. This paper systematically identifies three core challenges in characterizing MAPF’s empirical hardness: (1) instance-aware algorithm selection; (2) identification of structural features governing hardness—such as phase transitions, backbones, and backdoors; and (3) generation of high-hardness or diverse benchmark instances grounded in hardness understanding. Methodologically, we integrate empirical algorithm analysis, instance feature engineering, phase transition theory, and structured hardness modeling. Our key contribution is the first comprehensive empirical hardness analysis framework for MAPF, bridging the theory–practice divide. It enables interpretable algorithm selection, data-driven hardness prediction, and controllable benchmark generation—thereby laying a theoretical and technical foundation for adaptive multi-agent planning. (149 words)

Technology Category

• Multiagent Systems: Multiagent Planning
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Identifying best algorithms for specific MAPF instances
• Understanding instance features affecting empirical hardness
• Generating hard MAPF instances and diverse benchmarks

Innovation

• Algorithm selection for optimal MAPF solving
• Identifying key features affecting MAPF empirical hardness
• Generating hard MAPF instances using hardness knowledge