The development of connected and autonomous vehicles opens an opportunity to manage intersections without signals. One promising approach is to use a central autonomous intersection manager to optimize the movement of the vehicles in the intersection. Existing work uses Mixed Integer Linear Programming (MILP) to find optimal solutions for this problem but is time-consuming and cannot be applied in real-time. On the other hand, the coordination of the vehicles is essentially a Multi-Agent Path Finding (MAPF) problem, for which dozens of efficient algorithms have been proposed in recent years. Inspired by these MAPF algorithms, we propose a three-level algorithm called PSL to solve the intersection coordination problem. Theoretically, PSL is complete and polynomial-time in the number of vehicles. Empirically, PSL runs significantly faster with only a slight compromise in the solution quality than the optimal MILP method. It also generates significantly better solutions with a slightly larger runtime than the traditional First-Come-First-Served strategy.