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Multi-Candidate Carpooling Routing Problem and Its Approximation Algorithms

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Combinatorial Optimization and Applications (COCOA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14461))

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Abstract

Motivated by the carpooling services, we investigate a new and more challenging scenario for carpooling and model it as the Multi-candidate Carpooling Routing Problem (MCRP). The MCRP can be regarded as a new variant of TSP called Generalized Precedence-Constaint Asymmetric Subset Traveling Salesman Path Problem (GPAS-TSPP) and we construct complexity hierarchies for the related problems. We propose a 4-approximation algorithm for its special case Carpooling Routing Problem (CRP), followed by a (\(5+\epsilon \))-approximation algorithm for MCRP on the planar graph. We also design an exact algorithm based on dynamic programming to solve the general MCRP, serving as a benchmark. To the best of our knowledge, we are the first to explore the complexity hierarchy of carpooling problems in the TSP family and give constant-approximation algorithms for these new practical variants.

This work was supported by the National Key R &D Program of China [2020YFB1707900]; the National Natural Science Foundation of China [62272302, 62172276] and Shanghai Municipal Science and Technology Major Project [2021SHZDZX0102], and DiDi GAIA Research Collaboration Plan [202204]. Xiaofeng Gao is the corresponding author.

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Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Jiale Zhang, Xiuqi Huang, Zifeng Liu, Xiaofeng Gao & Guihai Chen

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  1. Jiale Zhang
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  2. Xiuqi Huang
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  3. Zifeng Liu
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  4. Xiaofeng Gao
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  5. Guihai Chen
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Correspondence to Jiale Zhang .

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Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Beijing Normal University, Zhuhai, China

    Jianxiong Guo

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Zhang, J., Huang, X., Liu, Z., Gao, X., Chen, G. (2024). Multi-Candidate Carpooling Routing Problem and Its Approximation Algorithms. In: Wu, W., Guo, J. (eds) Combinatorial Optimization and Applications. COCOA 2023. Lecture Notes in Computer Science, vol 14461. Springer, Cham. https://doi.org/10.1007/978-3-031-49611-0_27

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  • DOI: https://doi.org/10.1007/978-3-031-49611-0_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49610-3

  • Online ISBN: 978-3-031-49611-0

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