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Complexity and Approximation Results on the Shared Transportation Problem

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Combinatorial Optimization and Applications (COCOA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13135))

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Abstract

In our modern societies, a certain number of people do not own a car, by choice or by obligation. For some trips, there is no or few alternatives to the car. One way to make these trips possible for these people is to be transported by others who have already planned their trips. We propose to model this problem using as path-finding problem in a list edge-colored graph. This problem is a generalization of the \(s-t\)-path problem, studied by Böhmová et al. We study two optimization functions: minimizing the number of color changes and minimizing the number of colors. We study the complexity and the approximation of this problem. We show the existence of polynomial cases. We show that this problem is NP-complete and hard to approximate, even in restricted cases. Finally, we provide an approximation algorithm.

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Authors and Affiliations

  1. LIRMM, Univ Montpellier, CNRS, Montpellier, France

    Tom Davot, Rodolphe Giroudeau & Jean-Claude König

Authors
  1. Tom Davot
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  2. Rodolphe Giroudeau
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  3. Jean-Claude König
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Corresponding author

Correspondence to Tom Davot .

Editor information

Editors and Affiliations

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

    Ding-Zhu Du

  2. University of New Brunswick, Fredericton, NB, Canada

    Donglei Du

  3. Tianjin University of Technology, Tianjin, China

    Chenchen Wu

  4. Beijing University of Technology, Beijing, China

    Dachuan Xu

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Davot, T., Giroudeau, R., König, JC. (2021). Complexity and Approximation Results on the Shared Transportation Problem. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_12

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  • DOI: https://doi.org/10.1007/978-3-030-92681-6_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92680-9

  • Online ISBN: 978-3-030-92681-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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