International Workshop on Approximation and Online Algorithms

Approximation and Online Algorithms pp 72-83 | Cite as

Buyback Problem with Discrete Concave Valuation Functions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9499)


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.



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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Shun Fukuda
    • 1
  • Akiyoshi Shioura
    • 2
  • Takeshi Tokuyama
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Department of Social EngineeringTokyo Institute of TechnologyTokyoJapan

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