On the Np-Hardness of the Minimum Dispersion Routing Problem

Abstract

In the Minimum Dispersion Routing Problem, a set of vertices must be served by tours with trajectories defined in order to reduce the dispersion of vehicles. Tours must be related to each other and impose a spatial and temporal synchronization among vehicles, quantified by an original dispersion metric used in an objective function to be minimized. In this paper, we demonstrate that Euclidean Traveling Salesman Problem solutions can be found by MDRP solvers. We describe a method to reduce Euclidean Traveling Salesman Problem instances to Minimum Dispersion Routing Problem instances in polynomial time, proving that the last one is NP-Hard.