A New Constraint Satisfaction Perspective on Multi-Agent Path Finding

Abstract

In this paper, we adopt a new perspective on the Multi-Agent Path Finding (MAPF) problem and view it as a Constraint Satisfaction Problem (CSP). A variable corresponds to an agent, its domain is the set of all paths from the start vertex to the goal vertex of the agent, and the constraints allow only conflict-free paths for each pair of agents. Although the domains and constraints are only implicitly defined, this new CSP perspective allows us to use successful techniques from CSP search. With the concomitant idea of using matrix computations for calculating the size of the reduced domain of an uninstantiated variable, we apply Dynamic Variable Ordering and Rapid Random Restarts to the MAPF problem. In our experiments, the resulting simple polynomial-time MAPF solver, called Matrix MAPF solver, either outperforms or matches the performance of many state-of-the-art solvers for the MAPF problem and its variants.