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

Abstract

We have studied numerically the frequency distribution $\rho (n)$ 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 $\rho (n)$ on either the number of cities N or the dimension d.

6 pages, 3 figures. To be published in Int. J. Mod. Phys. C

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