Proportional Cost Buyback Problem with Weight Bounds

  • Yasushi Kawase
  • Xin Han
  • Kazuhisa Makino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9486)


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.


Knapsack Problem Competitive Ratio Element Weight Knapsack Constraint Weight Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Social EngineeringTokyo Institute of TechnologyTokyoJapan
  2. 2.Software SchoolDalian University of TechnologyDalianChina
  3. 3.Research Institute for Mathematical ScienceKyoto UniversityKyotoJapan

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