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Buyback Problem with Discrete Concave Valuation Functions

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Approximation and Online Algorithms (WAOA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9499))

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Abstract

We discuss an online discrete optimization problem called the buyback problem. In the literature of the buyback problem, the valuation function representing the value of a set of selected elements is given by a linear function. In this paper, we consider a generalization of the buyback problem using a nonlinear valuation function. We propose an online algorithm for the problem with a discrete concave valuation function, and show that it achieves the same competitive ratio as the best possible ratio for a linear valuation function.

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Acknowledgements

The authors thank anonymous referees for their valuable comments on the manuscript. This work is supported by JSPS/MEXT KAKENHI Grand Numbers 24106007, 25106503, 15H02665, 15H00848, 15K00030.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

    Shun Fukuda & Takeshi Tokuyama

  2. Department of Social Engineering, Tokyo Institute of Technology, Tokyo, 152-8550, Japan

    Akiyoshi Shioura

Authors
  1. Shun Fukuda
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  2. Akiyoshi Shioura
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  3. Takeshi Tokuyama
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Corresponding author

Correspondence to Akiyoshi Shioura .

Editor information

Editors and Affiliations

  1. University of Waterloo, Waterloo, Canada

    Laura Sanità

  2. Technische Universität Berlin, Berlin, Berlin, Germany

    Martin Skutella

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Fukuda, S., Shioura, A., Tokuyama, T. (2015). Buyback Problem with Discrete Concave Valuation Functions. In: Sanità, L., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2015. Lecture Notes in Computer Science(), vol 9499. Springer, Cham. https://doi.org/10.1007/978-3-319-28684-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-28684-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28683-9

  • Online ISBN: 978-3-319-28684-6

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