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Robust Online Algorithms for Certain Dynamic Packing Problems

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Approximation and Online Algorithms (WAOA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11926))

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Abstract

Online algorithms that allow a small amount of migration or recourse have been intensively studied in the last years. They are essential in the design of competitive algorithms for dynamic problems, where objects can also depart from the instance. In this work, we give a general framework to obtain so called robust online algorithms for a variety of dynamic problems: these online algorithms achieve an asymptotic competitive ratio of \(\gamma +\epsilon \) with migration \(O(1/\epsilon )\), where \(\gamma \) is the best known offline asymptotic approximation ratio. For our framework, we require only two ingredients: (i) the existence of an online algorithm for the static case (without departures) that provides a provably good solution compared to the total volume of the instance and (ii) that the optimal solution always exceeds this total volume. If these criteria are met, we can complement the online algorithm with any offline algorithm.

While these criteria are naturally fulfilled by many dynamic problems, they are especially suited for packing problems. In order to show the usefulness of our approach in this area, we improve upon the best known robust algorithms for the dynamic versions of generalizations of Strip Packing and Bin Packing, including the first robust algorithms for general d-dimensional Bin Packing and Vector Packing.

The authors thank Marten Maack and Malin Rau for initial discussions.

S. Berndt—Supported by DFG Project, “Robuste Online-Algorithmen für Scheduling- und Packungsprobleme”, JA 612/19-1.

K. Grage—Supported by GIF-Project “Polynomial Migration for Online Scheduling”.

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Authors and Affiliations

  1. Department of Computer Science, Kiel University, Kiel, Germany

    Sebastian Berndt, Kilian Grage, Klaus Jansen & Ingmar Knof

  2. University of Warwick, Coventry, UK

    Valentin Dreismann

Authors
  1. Sebastian Berndt
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  2. Valentin Dreismann
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  3. Kilian Grage
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  4. Klaus Jansen
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  5. Ingmar Knof
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Corresponding author

Correspondence to Kilian Grage .

Editor information

Editors and Affiliations

  1. LIP6, Sorbonne University, Paris, France

    Evripidis Bampis

  2. Department for Mathematics and Computer Science, University of Bremen, Bremen, Germany

    Nicole Megow

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Berndt, S., Dreismann, V., Grage, K., Jansen, K., Knof, I. (2020). Robust Online Algorithms for Certain Dynamic Packing Problems. In: Bampis, E., Megow, N. (eds) Approximation and Online Algorithms. WAOA 2019. Lecture Notes in Computer Science(), vol 11926. Springer, Cham. https://doi.org/10.1007/978-3-030-39479-0_4

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