Cutting glass

Janos Pach, Gabor Tardos

Research output: Contribution to conferencePaper

2 Citations (Scopus)


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 n1/3 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 languageEnglish
Number of pages10
Publication statusPublished - Jan 1 2000
Event16th Annual Symposium on Computational Geometry - Hong Kong, Hong Kong
Duration: Jun 12 2000Jun 14 2000


Other16th Annual Symposium on Computational Geometry
CityHong Kong, Hong Kong

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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    Pach, J., & Tardos, G. (2000). Cutting glass. 360-369. Paper presented at 16th Annual Symposium on Computational Geometry, Hong Kong, Hong Kong, .