The Euclidean travelling salesman problem: Frequency distribution of neighbours for small-size systems

Abstract

We have studied numerically the frequency distribution $ρ(n)$ of the n-th neighbour along the optimal tour in the Euclidean travelling salesman problem for N cities, in dimensions d=2 and d=3. We find there is no significant dependence of $ρ(n)$ on either the number of cities N or the dimension d.