Abstract We present an algorithm that computes the complete set of Pareto-optimal coordination strategies for two translating polygonal robots in the plane. A collision-free acyclic roadmap of piecewise-linear paths is given on which the two robots move. The robots have a maximum speed and are capable of instantly switching between any two arbitrary speeds. Each robot would like to minimize its travel time independently. The Pareto-optimal solutions are the ones for which there exist no solutions that are better for both robots. The algorithm computes exact solutions in time O(mn2 log n), in which m is the number of paths in the roadmap, n is the number of coordination space vertices. An implementation is presented.