On the Nearest Neighbor Algorithm for Mean Field Traveling Salesman Problem

Abstract : In this work we consider the mean field traveling salesman problem, where the intercity distances are taken to be i.i.d. with some distribution F. We consider the simplest approximation algorithm, namely, the nearest neighbor algorithm, that is to move to the nearest non-visited city. We show the limiting behavior of the total length of the nearest neighbor tour depends on the scaling properties of the density of F at 0 and derive the limits for all the possible cases for a general F.