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An Improved Algorithm for Open Online Dial-a-Ride

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Approximation and Online Algorithms (WAOA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13538))

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Abstract

We consider the open online dial-a-ride problem, where transportation requests appear online in a metric space and need to be served by a single server. The objective is to minimize the completion time until all requests have been served. We present a new, parameterized algorithm for this problem and prove that it attains a competitive ratio of \(1 + \varphi \approx 2.618\) for some choice of its parameter, where \(\varphi \) is the golden ratio. This improves the best known bounds for open online dial-a-ride both for general metric spaces as well as for the real line. We also give a lower bound of 2.457 for the competitive ratio of our algorithm for any parameter choice.

Supported by DFG grant DI 2041/2.

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Notes

  1. 1.

    If the server can distinguish the last request, it can start an optimal schedule once all requests are released, achieving a completion time of at most twice the optimum.

  2. 2.

    We adopt a strict definition of the competitive ratio that requires a bounded ratio for all request sequences, i.e., we do not allow an additive constant.

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Authors and Affiliations

  1. TU Darmstadt, Darmstadt, Germany

    Júlia Baligács, Yann Disser, Nils Mosis & David Weckbecker

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  1. Júlia Baligács
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  2. Yann Disser
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  3. Nils Mosis
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  4. David Weckbecker
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Correspondence to David Weckbecker .

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Editors and Affiliations

  1. Aalto University, Espoo, Finland

    Parinya Chalermsook

  2. Shanghai University of Finance and Economics, Shanghai, China

    Bundit Laekhanukit

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Baligács, J., Disser, Y., Mosis, N., Weckbecker, D. (2022). An Improved Algorithm for Open Online Dial-a-Ride. In: Chalermsook, P., Laekhanukit, B. (eds) Approximation and Online Algorithms. WAOA 2022. Lecture Notes in Computer Science, vol 13538. Springer, Cham. https://doi.org/10.1007/978-3-031-18367-6_8

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  • DOI: https://doi.org/10.1007/978-3-031-18367-6_8

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