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
VolumePart F129851
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

Other

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

Fingerprint

Transversals
Computing
Line segment
Line
Intersect
Family
Polygon

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 (Vol. Part F129851, pp. 71-80). Association for Computing Machinery. https://doi.org/10.1145/109648.109656

Computing shortest transversals of sets. / Bhattacharya, Binay; Czyzowicz, Jurek; Egyed, Peter; Stojmenovic, Ivan; Toussaint, Godfried; Urrutia, Jorge.

Proceedings of the Annual Symposium on Computational Geometry. Vol. Part F129851 Association for Computing Machinery, 1991. p. 71-80.

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

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. vol. Part F129851, Association for Computing Machinery, pp. 71-80, 7th Annual Symposium on Computational Geometry, SCG 1991, North Conway, United States, 6/10/91. https://doi.org/10.1145/109648.109656
Bhattacharya B, Czyzowicz J, Egyed P, Stojmenovic I, Toussaint G, Urrutia J. Computing shortest transversals of sets. In Proceedings of the Annual Symposium on Computational Geometry. Vol. Part F129851. Association for Computing Machinery. 1991. p. 71-80 https://doi.org/10.1145/109648.109656
Bhattacharya, Binay ; Czyzowicz, Jurek ; Egyed, Peter ; Stojmenovic, Ivan ; Toussaint, Godfried ; Urrutia, Jorge. / Computing shortest transversals of sets. Proceedings of the Annual Symposium on Computational Geometry. Vol. Part F129851 Association for Computing Machinery, 1991. pp. 71-80
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