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Proportional Cost Buyback Problem with Weight Bounds

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Combinatorial Optimization and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9486))

Abstract

In this paper, we study the proportional cost buyback problem. The input is a sequence of elements \(e_1,e_2,\dots ,e_n\), each of which has a weight \(w(e_i)\). We assume that weights have an upper and a lower bound, i.e., \(l\le w(e_i)\le u\) for any \(i\). Given the ith element \(e_i\), we either accept \(e_i\) or reject it with no cost, subject to some constraint on the set of accepted elements. During the iterations, we could cancel some previously accepted elements at a cost that is proportional to the total weight of them. Our goal is to maximize the profit, i.e., the sum of the weights of elements kept until the end minus the total cancellation cost occurred. We consider the matroid and unweighted knapsack constraints. For either case, we construct optimal online algorithms and prove that they are the best possible.

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Acknowledgments

The first author is supported by JSPS KAKENHI Grant Number 26887014 and JST, ERATO, Kawarabayashi Large Graph Project. The second author is supported by NFSC(11571060), RGC (HKU716412E) and the Fundamental Research Funds for the Central Universities (DUT15LK10). The last author is supported by JSPS KAKENHI Grant.

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Authors and Affiliations

  1. Department of Social Engineering, Tokyo Institute of Technology, Tokyo, Japan

    Yasushi Kawase

  2. Software School, Dalian University of Technology, Dalian, China

    Xin Han

  3. Research Institute for Mathematical Science, Kyoto University, Kyoto, Japan

    Kazuhisa Makino

Authors
  1. Yasushi Kawase
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  2. Xin Han
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  3. Kazuhisa Makino
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Corresponding author

Correspondence to Yasushi Kawase .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Marywood University, Scranton, Pennsylvania, USA

    Zaixin Lu

  2. North Carolina Central University, Durham, North Carolina, USA

    Donghyun Kim

  3. University of Texas at Dallas, Richardson, Texas, USA

    Weili Wu

  4. Texas Southern University, Houston, Texas, USA

    Wei Li

  5. University of Texas at Dallas, Richardson, Texas, USA

    Ding-Zhu Du

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Kawase, Y., Han, X., Makino, K. (2015). Proportional Cost Buyback Problem with Weight Bounds. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, DZ. (eds) Combinatorial Optimization and Applications. Lecture Notes in Computer Science(), vol 9486. Springer, Cham. https://doi.org/10.1007/978-3-319-26626-8_59

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  • DOI: https://doi.org/10.1007/978-3-319-26626-8_59

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26625-1

  • Online ISBN: 978-3-319-26626-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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