On Inducing Polygons and Related Problems

  • Eyal Ackerman
  • Rom Pinchasi
  • Ludmila Scharf
  • Marc Scherfenberg
Conference paper

DOI: 10.1007/978-3-642-04128-0_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5757)
Cite this paper as:
Ackerman E., Pinchasi R., Scharf L., Scherfenberg M. (2009) On Inducing Polygons and Related Problems. In: Fiat A., Sanders P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg

Abstract

Bose et al. [1] asked whether for every simple arrangement \(\mathcal{A}\) of n lines in the plane there exists a simple n-gon P that induces\(\mathcal{A}\) by extending every edge of P into a line. We prove that such a polygon always exists and can be found in O(n logn) time. In fact, we show that every finite family of curves \(\mathcal{C}\) such that every two curves intersect at least once and finitely many times and no three curves intersect at a single point possesses the following Hamiltonian-type property: the union of the curves in \(\mathcal{C}\) contains a simple cycle that visits every curve in \(\mathcal{C}\) exactly once.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Eyal Ackerman
    • 1
  • Rom Pinchasi
    • 2
  • Ludmila Scharf
    • 1
  • Marc Scherfenberg
    • 1
  1. 1.Institute of Computer ScienceFreie Universität BerlinBerlinGermany
  2. 2.Mathematics DepartmentTechnion—Israel Institute of TechnologyHaifaIsrael

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