Computing shortest transversals of sets

Binay Bhattacharya, Jurek Czyzowicz, Peter Egyed, Ivan Stojmenovic, Godfried Toussaint, Jorge Urrutia

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a family of objects in the plane, the line transversal problem is to compute a line that intersects every member of the family. In this paper we examine a variation of the line transversal problem that involves computing a shortest line segment that intersects every member of the family. In particular, we give O(nlogn) time algorithms for computing a shortest transversal of a family of n lines and of a family of n line segments. We also present an O(n log2 n) time algorithm for computing a shortest transversal of a family of polygons with a total of n vertices. In general, finding a line transversal for a family of n objects takes Ω(n log n) time. This time bound holds for a family of n line segments thus our shortest transversal algorithm for this family is optimal.

Original languageEnglish (US)
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
PublisherAssociation for Computing Machinery
Pages71-80
Number of pages10
ISBN (Print)0897914260
DOIs
StatePublished - Jun 1 1991
Event7th Annual Symposium on Computational Geometry, SCG 1991 - North Conway, United States
Duration: Jun 10 1991Jun 12 1991

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Other

Other7th Annual Symposium on Computational Geometry, SCG 1991
CountryUnited States
CityNorth Conway
Period6/10/916/12/91

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Bhattacharya, B., Czyzowicz, J., Egyed, P., Stojmenovic, I., Toussaint, G., & Urrutia, J. (1991). Computing shortest transversals of sets. In Proceedings of the Annual Symposium on Computational Geometry (pp. 71-80). (Proceedings of the Annual Symposium on Computational Geometry). Association for Computing Machinery. https://doi.org/10.1145/109648.109656