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Robust Online Algorithms for Dynamic Choosing Problems

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Connecting with Computability (CiE 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12813))

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Abstract

Semi-online algorithms that are allowed to perform a bounded amount of repacking achieve guaranteed good worst-case behaviour in a more realistic setting. Most of the previous works focused on minimization problems that aim to minimize some costs. In this work, we study maximization problems that aim to maximize their profit.

We mostly focus on a class of problems that we call choosing problems, where a maximum profit subset of a set objects has to be maintained. Many known problems, such as Knapsack, MaximumIndependentSet and variations of these, are part of this class. We present a framework for choosing problems that allows us to transfer offline \(\alpha \)-approximation algorithms into \((\alpha -\epsilon )\)-competitive semi-online algorithms with amortized migration \(O(1/\epsilon )\). Moreover we complement these positive results with lower bounds that show that our results are tight in the sense that no amortized migration of \(o(1/\epsilon )\) is possible.

Supported by DFG-Project JA 612 /19-1 and GIF-Project “Polynomial Migration for Online Scheduling”. A full version of the paper is available at http://arxiv.org/abs/2104.09803.

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Author information

Authors and Affiliations

  1. University of Lübeck, 23562, Lübeck, Germany

    Sebastian Berndt

  2. Kiel University, 24118, Kiel, Germany

    Kilian Grage, Klaus Jansen & Lukas Johannsen

  3. Göttingen University, 37073, Göttingen, Germany

    Maria Kosche

Authors
  1. Sebastian Berndt
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  2. Kilian Grage
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  3. Klaus Jansen
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  4. Lukas Johannsen
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  5. Maria Kosche
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Corresponding author

Correspondence to Kilian Grage .

Editor information

Editors and Affiliations

  1. University of Lille, Lille, France

    Liesbeth De Mol

  2. Vakgroep Wiskunde, Ghent University, Ghent, Belgium

    Andreas Weiermann

  3. University of Göttingen, Göttingen, Germany

    Florin Manea

  4. Ghent University, Ghent, Belgium

    David Fernández-Duque

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Berndt, S., Grage, K., Jansen, K., Johannsen, L., Kosche, M. (2021). Robust Online Algorithms for Dynamic Choosing Problems. In: De Mol, L., Weiermann, A., Manea, F., Fernández-Duque, D. (eds) Connecting with Computability. CiE 2021. Lecture Notes in Computer Science(), vol 12813. Springer, Cham. https://doi.org/10.1007/978-3-030-80049-9_4

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  • DOI: https://doi.org/10.1007/978-3-030-80049-9_4

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  • Print ISBN: 978-3-030-80048-2

  • Online ISBN: 978-3-030-80049-9

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