### 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 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*Information Processing Letters*,

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