New Distance Constraint Makes Multi-Agent Pathfinding PSPACE-Complete
Agents must stay at least r+1 apart at all times—but algorithms still handle hundreds.
A new paper from researchers Takahiro Suzuki, Yuma Tamura, and Keisuke Okumura tackles a harder variant of multi-agent pathfinding (MAPF) called Distance-r Independent Unlabeled MAPF. In this problem, agents must maintain a pairwise distance of at least r+1 at all times—a constraint that models real-world needs like collision avoidance, communication range, or safe spacing in drone swarms. The team proves that adding this constraint pushes the feasibility problem from polynomial-time to PSPACE-complete, meaning it is fundamentally harder than standard unlabeled MAPF.
Despite the theoretical hardness, the authors propose two complementary approaches: a reduction-based optimal algorithm with a feasibility-preserving compression procedure, and a configuration generator-based search. Empirical results show that their methods can handle hundreds of agents within a practical timeframe, making the work immediately relevant for applications in warehouse robotics, autonomous vehicle coordination, and multi-robot systems where spacing is critical.
- Problem is PSPACE-complete vs. polynomial for standard unlabeled MAPF
- Distance constraint r+1 generalizes collision modeling for real-world coordination
- Algorithm handles hundreds of agents despite theoretical intractability
Why It Matters
Enables safe, distance-constrained coordination for swarms of drones, robots, and autonomous vehicles at scale.