The Centred Traveling Salesman at Finite Temperature

TL;DR

This paper applies a statistical mechanics approach to analyze the phase transition in a generalized Traveling Salesman Problem, revealing a crossover behavior and a unique duality in the solution at finite temperatures.

Contribution

It introduces a novel application of statistical mechanics to the centred TSP, highlighting phase transition phenomena and solution duality at finite temperatures.

Findings

Evidence of a phase crossover in the centred TSP

Method detects signs of transition at finite temperatures

Reveals a duality in the problem's solution

Abstract

A recently formulated statistical mechanics method is used to study the phase transition occurring in a generalisation of the Traveling Salesman Problem (TSP) known as the centred TSP. The method shows that the problem has clear signs of a crossover, but is only able to access (unscaled) finite temperatures above the transition point. The solution of the problem using this method displays a curious duality.