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Symmetry breaking in optimal transport networks

Author

Listed:
  • Siddharth Patwardhan

    (Indiana University)

  • Marc Barthelemy

    (Institut de Physique Théorique
    Centre d’Analyse et de Mathématique Sociales (CNRS/EHESS) 54 Avenue de Raspail)

  • Şirag Erkol

    (Northwestern University)

  • Santo Fortunato

    (Indiana University)

  • Filippo Radicchi

    (Indiana University)

Abstract

Engineering multilayer networks that efficiently connect sets of points in space is a crucial task in all practical applications that concern the transport of people or the delivery of goods. Unfortunately, our current theoretical understanding of the shape of such optimal transport networks is quite limited. Not much is known about how the topology of the optimal network changes as a function of its size, the relative efficiency of its layers, and the cost of switching between layers. Here, we show that optimal networks undergo sharp transitions from symmetric to asymmetric shapes, indicating that it is sometimes better to avoid serving a whole area to save on switching costs. Also, we analyze the real transportation networks of the cities of Atlanta, Boston, and Toronto using our theoretical framework and find that they are farther away from their optimal shapes as traffic congestion increases.

Suggested Citation

  • Siddharth Patwardhan & Marc Barthelemy & Şirag Erkol & Santo Fortunato & Filippo Radicchi, 2024. "Symmetry breaking in optimal transport networks," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
  • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-48068-9
    DOI: 10.1038/s41467-024-48068-9
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Mattia Mazzoli & Alex Molas & Aleix Bassolas & Maxime Lenormand & Pere Colet & José J. Ramasco, 2019. "Field theory for recurrent mobility," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    3. Michael Mc Gettrick, 2020. "Correction to: The role of city geometry in determining the utility of a small urban light rail/tram system," Public Transport, Springer, vol. 12(3), pages 517-518, October.
    4. Angeloudis, Panagiotis & Fisk, David, 2006. "Large subway systems as complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 553-558.
    5. Latora, Vito & Marchiori, Massimo, 2002. "Is the Boston subway a small-world network?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 109-113.
    6. Katherine A. McCulloh & John S. Sperry & Frederick R. Adler, 2003. "Water transport in plants obeys Murray's law," Nature, Nature, vol. 421(6926), pages 939-942, February.
    7. Sybil Derrible, 2012. "Network Centrality of Metro Systems," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-10, July.
    8. Jon M. Kleinberg, 2000. "Navigation in a small world," Nature, Nature, vol. 406(6798), pages 845-845, August.
    9. Yuriy Mileyko & Herbert Edelsbrunner & Charles A Price & Joshua S Weitz, 2012. "Hierarchical Ordering of Reticular Networks," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-9, June.
    10. Marta C. González & César A. Hidalgo & Albert-László Barabási, 2009. "Understanding individual human mobility patterns," Nature, Nature, vol. 458(7235), pages 238-238, March.
    11. Michael Mc Gettrick, 2020. "The role of city geometry in determining the utility of a small urban light rail/tram system," Public Transport, Springer, vol. 12(1), pages 233-259, March.
    12. Sybil Derrible & Christopher Kennedy, 2010. "Characterizing metro networks: state, form, and structure," Transportation, Springer, vol. 37(2), pages 275-297, March.
    13. Dirk Helbing & Joachim Keltsch & Péter Molnár, 1997. "Modelling the evolution of human trail systems," Nature, Nature, vol. 388(6637), pages 47-50, July.
    14. Zhang, Jianhua & Xu, Xiaoming & Hong, Liu & Wang, Shuliang & Fei, Qi, 2011. "Networked analysis of the Shanghai subway network, in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4562-4570.
    15. David-Maximilian Storch & Marc Timme & Malte Schröder, 2021. "Incentive-driven transition to high ride-sharing adoption," Nature Communications, Nature, vol. 12(1), pages 1-10, December.
    16. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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