Skip to main content

Cutting Glass

Abstract.

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. We also consider the special cases when the family consists of intervals, axis-parallel rectangles, ``fat'' sets, or ``fat'' sets with bounded size.

Author information

Authors and Affiliations

Authors

Additional information

Received April 7, 1999. Online publication May 16, 2000.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pach, J., Tardos, G. Cutting Glass . Discrete Comput Geom 24, 481–496 (2000). https://doi.org/10.1007/s004540010050

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s004540010050

Keywords

  • Pairwise Disjoint
  • Compact Convex
  • Constant Fraction