From the Physics of Interacting Polymers to Optimizing Routes on the London Underground

TL;DR

This paper introduces a physics-inspired, distributed routing algorithm that considers all path choices simultaneously, improving network path optimization across various real-world systems like the London Underground.

Contribution

It develops a novel, generic routing algorithm based on the physics of interacting polymers, capable of handling complex, large-scale network optimization problems.

Findings

Effective routing on Internet-like networks demonstrated

Application to London Underground data shows improved path efficiency

Analytical insights reveal phase transitions and scaling laws

Abstract

Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing algorithms optimize paths individually, thus providing sub-optimal solutions. We employ the physics of interacting polymers and disordered systems to analyze macroscopic properties of generic path-optimization problems and derive a simple, principled, generic and distributed routing algorithm capable of considering simultaneously all individual path choices. We demonstrate the efficacy of the new algorithm by applying it to: (i) random graphs resembling Internet overlay networks; (ii) travel on the London underground network based on Oyster-card data; and (iii) the global airport network. Analytically derived macroscopic properties give rise to insightful new routing phenomena, including phase transitions and scaling laws, which facilitate better understanding of the appropriate operational regimes and their limitations that are difficult to obtain otherwise.