## Abstract

We study the parameterized complexity of MINIMUM VOLUME PACKING and STRIP PACKING. In the two dimensional version the input consists of a set of rectangles S with integer side lengths. In the MINIMUM VOLUME PACKING problem, given a set of rectangles S and a number k, the goal is to decide if the rectangles can be packed in a bounding box of volume at most k. In the STRIP PACKING problem we are given a set of rectangles S, numbers W and k; the objective is to find if all the rectangles can be packed in a box of dimensions W×k. We prove that the 2-dimensional VOLUME PACKING is in FPT by giving an algorithm that runs in (2⋅2)^{k}⋅k^{O(1)} time. We also show that STRIP PACKING is W[1]-hard even in two dimensions and give an FPT algorithm for a special case of STRIP PACKING. Some of our results hold for the problems defined in higher dimensions as well.

Original language | English |
---|---|

Pages (from-to) | 56-64 |

Number of pages | 9 |

Journal | Theoretical Computer Science |

Volume | 661 |

DOIs | |

State | Published - 24 Jan 2017 |

Externally published | Yes |

## Keywords

- Greedy packing
- Strip Packing
- Volume minimization

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science