On piercing sets of objects

Matthew J. Katz, Franck Nielsen

Research output: Contribution to conferencePaperpeer-review

11 Scopus citations


A set of objects is k-pierceable if there exists a set of k points such that each object is pierced by (contains) at least one of these points. Finding the smallest integer k such that a set is k-pierceable is NP-complete. In this paper, we present efficient algorithms for finding a piercing set (i.e., a set of k points as above) for several classes of convex objects and small values of k. In some of the cases, our algorithms imply known as well as new Helly-type theorems, thus adding to previous results of Danzer and Gruenbaum who studied the case of axis-parallel boxes. The problems studied here are related to the collection of optimization problems in which one seeks the smallest scaling factor of a centrally symmetric convex object K, so that a set of points can be covered by k congruent homothets of K.

Original languageEnglish
Number of pages9
StatePublished - 1 Jan 1996
Externally publishedYes
EventProceedings of the 1996 12th Annual Symposium on Computational Geometry - Philadelphia, PA, USA
Duration: 24 May 199626 May 1996


ConferenceProceedings of the 1996 12th Annual Symposium on Computational Geometry
CityPhiladelphia, PA, USA

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics


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