From the physics of interacting polymers to optimizing routes on the London Underground

Chi H. Yeung*, David Saad, K.Y. Michael Wong

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    Optimizing paths on networks is crucial for many applications, ranging from subway traffic to Internet communication. Because global path optimization that takes account of all path choices simultaneously is computationally hard, most existing routing algorithms optimize paths individually, thus providing suboptimal solutions. We use 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 all individual path choices simultaneously. We demonstrate the efficacy of the 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, that facilitate better understanding of the appropriate operational regimes and their limitations, which are difficult to obtain otherwise.

    Original languageEnglish
    Pages (from-to)13717-13722
    Number of pages6
    JournalProceedings of the National Academy of Sciences
    Issue number34
    Early online date29 Jul 2013
    Publication statusPublished - 20 Aug 2013


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