### Abstract

J. Urrutia asked the following question. Given a family of pairwise disjoint compact convex sets on a sheet of glass, is it true that one can always separate from one another a constant fraction of them using edge-to-edge straight-line cuts? We answer this question in the negative, and establish some lower and upper bounds for the number of separable sets. In particular, we show that any family F of n pairwise disjoint convex polygons has at least n^{1/3} separable members, and a subfamily with this property can be constructed in O(N+n log n) time, where N denotes the total number of sides of F. We also consider the special cases when the family consists of intervals, axis-parallel rectangles, `fat' sets, or `fat' sets with bounded size.

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

Pages | 360-369 |

Number of pages | 10 |

Publication status | Published - Jan 1 2000 |

Event | 16th Annual Symposium on Computational Geometry - Hong Kong, Hong Kong Duration: Jun 12 2000 → Jun 14 2000 |

### Other

Other | 16th Annual Symposium on Computational Geometry |
---|---|

City | Hong Kong, Hong Kong |

Period | 6/12/00 → 6/14/00 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

## Fingerprint Dive into the research topics of 'Cutting glass'. Together they form a unique fingerprint.

## Cite this

*Cutting glass*. 360-369. Paper presented at 16th Annual Symposium on Computational Geometry, Hong Kong, Hong Kong, .