Fluctuations in the Site Disordered Traveling Salesman Problem

TL;DR

This paper extends a statistical mechanical approach to the site disordered traveling salesman problem, analyzing fluctuations around saddle points to better understand minimal path lengths.

Contribution

It introduces a discrete site disordered model and computes fluctuations, clarifying previous theoretical treatments and highlighting challenges in the zero temperature limit.

Findings

Fluctuations around saddle points can be computed in the model

The results clarify the theoretical basis of the approach

Difficulties remain in taking the zero temperature limit

Abstract

We extend a previous statistical mechanical treatment of the traveling salesman problem by defining a discrete "site disordered'' problem in which fluctuations about saddle points can be computed. The results clarify the basis of our original treatment, and illuminate but do not resolve the difficulties of taking the zero temperature limit to obtain minimal path lengths.