Optimal Multi-Agent Path Finding via Optimal Transport Collapses to Polynomial LP

arXiv·low signal

Shows that anonymous multi-agent path finding (MAPF) can be cast as multi-marginal optimal transport with Markovian structure, reducing the exponentially large problem to a polynomial-size linear program. The Schrödinger Bridge formulation enables scalable, optimal coordination of robot swarms on graphs. Primarily robotics-focused but the mathematical connection between MAPF and optimal transport opens new algorithmic approaches for any multi-agent coordination problem.