paper

The stochastic traveling salesman problem: Finite size scaling and the cavity prediction

arXiv:cond-mat/9802295 · doi:10.1023/A:1004570713967

Abstract

We study the random link traveling salesman problem, where lengths l_ij between city i and city j are taken to be independent, identically distributed random variables. We discuss a theoretical approach, the cavity method, that has been proposed for finding the optimal tour length over this random ensemble, given the assumption of replica symmetry. Using finite size scaling and a renormalized model, we test the cavity predictions against the results of simulations, and find excellent agreement over a range of distributions. We thus provide numerical evidence that the replica symmetric solution to this problem is the correct one. Finally, we note a surprising result concerning the distribution of kth-nearest neighbor links in optimal tours, and invite a theoretical understanding of this phenomenon.

21 pages, 7 figures; to appear in Journal of Statistical Physics (March 1999); this revision contains final version incorporating some changes

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