An Approximation Algorithm for the Curvature-Constrained Traveling Salesman Problem

We present an approximation algorithm for the Traveling Salesman Problem when the vehicle is constrained to move forward along paths with bounded curvature (Dubins’ vehicle). A deterministic algorithm returns in time O(n3) a tour within (( 1 + max { 8πρ Dmin , 14 3 }) log n ) of the optimum tour, where n is the number of points to visit, ρ is the minimum turning radius and Dmin is the minimum Euclidean distance between any two points. A randomized version returns a tour with an expected approximation ratio of (( 1 + 13.58ρ Dmin ) log n ) . This very simple algorithm reduces the Traveling Salesman Problem for Dubins’ vehicle to an Asymmetric Traveling Salesman Problem on a directed graph.