### Abstract

We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS forthe problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves.We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the perimeter of the convex enclosure. We also give efficient algorithms to find the smallest rectangle simultaneously enclosing a given pair of convex polygons.

Original language | English (US) |
---|---|

Pages (from-to) | 689-714 |

Number of pages | 26 |

Journal | Theory of Computing Systems |

Volume | 54 |

Issue number | 4 |

DOIs | |

State | Published - 2014 |

### Keywords

- Computational geometry
- Enclosure
- Packing

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics

## Fingerprint Dive into the research topics of 'Scandinavian thins on top of cake: New and improved algorithms for stacking and packing'. Together they form a unique fingerprint.

## Cite this

*Theory of Computing Systems*,

*54*(4), 689-714. https://doi.org/10.1007/s00224-013-9493-9