### Abstract

In bin-packing problems, given items need to be packed using a minimum number of bins. Inverse bin-packing number problems,IBPNfor short, assume a given set of items and number of bins. The objective is to achieve the minimum perturbation to the item-size vector so that all the items can be packed into the prescribed number of bins. In this paper, complexity status and approximation behavior for IBPN were investigated. Under the L_{p}-norm, p ∈{1, 2, ⋯,∞},IBPN turns out to be NP-hard in the strong sense.IBPNunder the L1-norm admits a polynomial time differential approximation scheme, and a fully polynomial time approximation scheme if a constant number of machines is provided as input. We also consider another IBPN variant where a specified feasible solution is given instead of a target bin number. The objective is to make the given solution optimal with minimum modification. We provide the hardness result for this problem.

Original language | English |
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Pages (from-to) | 60-68 |

Number of pages | 9 |

Journal | Information Processing Letters |

Volume | 115 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 Jan |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

### Cite this

*Information Processing Letters*,

*115*(1), 60-68. https://doi.org/10.1016/j.ipl.2014.09.005

}

*Information Processing Letters*, vol. 115, no. 1, pp. 60-68. https://doi.org/10.1016/j.ipl.2014.09.005

**Notes on inverse bin-packing problems.** / Chung, Yerim; Park, Myoung Ju.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Notes on inverse bin-packing problems

AU - Chung, Yerim

AU - Park, Myoung Ju

PY - 2015/1

Y1 - 2015/1

N2 - In bin-packing problems, given items need to be packed using a minimum number of bins. Inverse bin-packing number problems,IBPNfor short, assume a given set of items and number of bins. The objective is to achieve the minimum perturbation to the item-size vector so that all the items can be packed into the prescribed number of bins. In this paper, complexity status and approximation behavior for IBPN were investigated. Under the Lp-norm, p ∈{1, 2, ⋯,∞},IBPN turns out to be NP-hard in the strong sense.IBPNunder the L1-norm admits a polynomial time differential approximation scheme, and a fully polynomial time approximation scheme if a constant number of machines is provided as input. We also consider another IBPN variant where a specified feasible solution is given instead of a target bin number. The objective is to make the given solution optimal with minimum modification. We provide the hardness result for this problem.

AB - In bin-packing problems, given items need to be packed using a minimum number of bins. Inverse bin-packing number problems,IBPNfor short, assume a given set of items and number of bins. The objective is to achieve the minimum perturbation to the item-size vector so that all the items can be packed into the prescribed number of bins. In this paper, complexity status and approximation behavior for IBPN were investigated. Under the Lp-norm, p ∈{1, 2, ⋯,∞},IBPN turns out to be NP-hard in the strong sense.IBPNunder the L1-norm admits a polynomial time differential approximation scheme, and a fully polynomial time approximation scheme if a constant number of machines is provided as input. We also consider another IBPN variant where a specified feasible solution is given instead of a target bin number. The objective is to make the given solution optimal with minimum modification. We provide the hardness result for this problem.

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U2 - 10.1016/j.ipl.2014.09.005

DO - 10.1016/j.ipl.2014.09.005

M3 - Article

AN - SCOPUS:84908200332

VL - 115

SP - 60

EP - 68

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 1

ER -