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Improved Bounds for Open Online Dial-a-Ride on the Line

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Abstract

We consider the open, non-preemptive online Dial-a-Ride problem on the real line, where transportation requests appear over time and need to be served by a single server. We give a lower bound of 2.0585 on the competitive ratio, which is the first bound that strictly separates open online Dial-a-Ride on the line from open online TSP on the line in terms of competitive analysis, and is the best currently known lower bound even for general metric spaces. On the other hand, we present an algorithm that improves the best known upper bound from 2.9377 to 2.6662. The analysis of our algorithm is tight.

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Notes

  1. Note that this crucially needs that the capacity is bounded.

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Authors and Affiliations

  1. Darmstadt, Germany

    Alexander Birx

  2. Institute of Mathematics and Graduate School CE, TU Darmstadt, Darmstadt, Germany

    Yann Disser

  3. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Kevin Schewior

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  1. Alexander Birx
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  2. Yann Disser
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  3. Kevin Schewior
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Correspondence to Kevin Schewior.

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In part supported by the ‘Excellence Initiative’ of the German Federal and State Governments and the Graduate School CE at TU Darmstadt. Also in part supported by the Independent Research Fund Denmark, Natural Sciences, Grant DFF-0135-00018B.

A preliminary version of this article appeared in [8].

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Birx, A., Disser, Y. & Schewior, K. Improved Bounds for Open Online Dial-a-Ride on the Line. Algorithmica 85, 1372–1414 (2023). https://doi.org/10.1007/s00453-022-01061-4

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