Buyback problem with discrete concave valuation functions

Shun Fukuda; Akiyoshi Shioura; Takeshi Tokuyama

doi:10.1007/978-3-319-28684-6_7

Buyback problem with discrete concave valuation functions

Shun Fukuda, Akiyoshi Shioura, Takeshi Tokuyama

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

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.

Original language	English
Title of host publication	Approximation and Online Algorithms - 13th International Workshop, WAOA 2015, Revised Selected Papers
Editors	Martin Skutella, Laura Sanità
Publisher	Springer Verlag
Pages	72-83
Number of pages	12
ISBN (Print)	9783319286839
DOIs	https://doi.org/10.1007/978-3-319-28684-6_7
Publication status	Published - 2015
Event	13th International Workshop on Approximation and Online Algorithms, WAOA 2015 - Patras, Greece Duration: 2015 Sep 17 → 2015 Sep 18

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9499
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	13th International Workshop on Approximation and Online Algorithms, WAOA 2015
Country/Territory	Greece
City	Patras
Period	15/9/17 → 15/9/18

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-319-28684-6_7

Cite this

Fukuda, S., Shioura, A., & Tokuyama, T. (2015). Buyback problem with discrete concave valuation functions. In M. Skutella, & L. Sanità (Eds.), Approximation and Online Algorithms - 13th International Workshop, WAOA 2015, Revised Selected Papers (pp. 72-83). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9499). Springer Verlag. https://doi.org/10.1007/978-3-319-28684-6_7

Buyback problem with discrete concave valuation functions. / Fukuda, Shun; Shioura, Akiyoshi; Tokuyama, Takeshi.

Approximation and Online Algorithms - 13th International Workshop, WAOA 2015, Revised Selected Papers. ed. / Martin Skutella; Laura Sanità. Springer Verlag, 2015. p. 72-83 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9499).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Fukuda, S, Shioura, A & Tokuyama, T 2015, Buyback problem with discrete concave valuation functions. in M Skutella & L Sanità (eds), Approximation and Online Algorithms - 13th International Workshop, WAOA 2015, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9499, Springer Verlag, pp. 72-83, 13th International Workshop on Approximation and Online Algorithms, WAOA 2015, Patras, Greece, 15/9/17. https://doi.org/10.1007/978-3-319-28684-6_7

Fukuda S, Shioura A, Tokuyama T. Buyback problem with discrete concave valuation functions. In Skutella M, Sanità L, editors, Approximation and Online Algorithms - 13th International Workshop, WAOA 2015, Revised Selected Papers. Springer Verlag. 2015. p. 72-83. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-28684-6_7

Fukuda, Shun ; Shioura, Akiyoshi ; Tokuyama, Takeshi. / Buyback problem with discrete concave valuation functions. Approximation and Online Algorithms - 13th International Workshop, WAOA 2015, Revised Selected Papers. editor / Martin Skutella ; Laura Sanità. Springer Verlag, 2015. pp. 72-83 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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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AB - 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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Buyback problem with discrete concave valuation functions

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