The statistical mechanics of traveling salesman type problems

TL;DR

This paper analyzes the statistical mechanics of Hamiltonian paths, including the traveling salesman problem, in large systems without relying on the replica method, providing new insights into their thermodynamic properties.

Contribution

It introduces a novel analytical approach to study the statistical mechanics of TSP-like problems at finite temperature without the replica method.

Findings

Provides a large-N analytical framework

Applies to TSP and similar Hamiltonian path problems

Offers insights into the thermodynamics of complex path optimization

Abstract

We study the finite temperature statistical mechanics of Hamiltonian paths between a set of N quenched randomly distributed points in a finite domain D. The energy of the path is a function of the distance between neighboring points on the path, an example is the traveling salesman problem where the energy is the total distance between neighboring points on the path. We show how the system can be analyzed in the limit of large N without using the replica method.