Buyback problem with discrete concave valuation functions

Shun Fukuda, Akiyoshi Shioura, Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We discuss an online discrete optimization problem called the buyback problem. In the literature of the buyback problem, the valuation function representing the total value of selected elements is given by a linear function. In this paper, we consider a generalization of the buyback problem using nonlinear valuation functions. We propose an online algorithm for the problem with discrete concave valuation functions, and show that it achieves the tight competitive ratio, i.e., the competitive ratio of the proposed algorithm is equal to the known lower bound for the problem.

Original languageEnglish
Pages (from-to)78-96
Number of pages19
JournalDiscrete Optimization
Publication statusPublished - 2017 Nov


  • Buyback problem
  • Discrete concave function
  • Gross substitutes valuation
  • Matroid
  • Online discrete optimization problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics


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