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A Backtracking Algorithm for Solving the Nearly Equitable Strong Edge-coloring Problem on Transportation Network

Author

Listed:
  • Kai Zhang

    (The Hong Kong Polytechnic University
    Southeast University, Jiulonghu Campus)

  • Yu Dong

    (Southeast University, Jiulonghu Campus)

  • Lin Cheng

    (Southeast University, Jiulonghu Campus)

  • Xinyuan Chen

    (Nanjing University of Aeronautics and Astronautics)

  • Qixiu Cheng

    (University of Bristol)

  • Zhiyuan Liu

    (Southeast University, Jiulonghu Campus)

Abstract

Faced with the challenges of continuously expanding traffic network scales and increasing travel demands in practical engineering problems, the computation required by traditional algorithms for solving large-scale traffic assignment problem (TAP) is expanding, making it increasingly difficult to balance computational efficiency and accuracy. The search for effective decomposition methods suitable for large-scale TAP has been a prominent focus. However, the complexity of the transportation network topology makes it challenging for existing traffic assignment algorithms to decompose the network. This paper utilizes the edge color theory from graph theory, the topology of transportation networks is deeply analyzed, and the characteristics of two-way edge coloring are defined in transportation networks. To further decompose the network at the level of link variables, a backtracking algorithm is presented for solving the nearly equitable strong edge-coloring (NESEC) problem. The proposed algorithm provides a theoretical foundation for modeling parallel traffic assignment based on the alternative direction method of multipliers (ADMM). The backtracking algorithm makes NESEC results easier for the ADMM-based traffic assignment model to perform parallel computation and enables the parallel calculation on thousands of link-based subproblems on large-scale TAP. The proposed algorithm was validated by conducting numerical experiments.

Suggested Citation

  • Kai Zhang & Yu Dong & Lin Cheng & Xinyuan Chen & Qixiu Cheng & Zhiyuan Liu, 2025. "A Backtracking Algorithm for Solving the Nearly Equitable Strong Edge-coloring Problem on Transportation Network," Networks and Spatial Economics, Springer, vol. 25(1), pages 219-248, March.
    • Handle: RePEc:kap:netspa:v:25:y:2025:i:1:d:10.1007_s11067-024-09661-z
    DOI: 10.1007/s11067-024-09661-z
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    References listed on IDEAS

    as
    1. Liu, Zhiyuan & Chen, Xinyuan & Hu, Jintao & Wang, Shuaian & Zhang, Kai & Zhang, Honggang, 2023. "An alternating direction method of multipliers for solving user equilibrium problem," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1072-1084.
    2. Roberto Scazzieri, 2022. "Decomposability and Relative Invariance: the Structural Approach to Network Complexity and Resilience," Networks and Spatial Economics, Springer, vol. 22(3), pages 635-657, September.
    3. Rui Ding & Norsidah Ujang & Hussain Bin Hamid & Mohd Shahrudin Abd Manan & Rong Li & Safwan Subhi Mousa Albadareen & Ashkan Nochian & Jianjun Wu, 2019. "Application of Complex Networks Theory in Urban Traffic Network Researches," Networks and Spatial Economics, Springer, vol. 19(4), pages 1281-1317, December.
    4. Fabrizio Borghini & Isabel Méndez-Díaz & Paula Zabala, 2020. "An exact algorithm for the edge coloring by total labeling problem," Annals of Operations Research, Springer, vol. 286(1), pages 11-31, March.
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