On inducing polygons and related problems

Eyal Ackerman, Rom Pinchasi, Ludmila Scharf, Marc Scherfenberg

Research output: Contribution to journalArticlepeer-review


Bose et al. (2003) [2] asked whether for every simple arrangement A of n lines in the plane there exists a simple n-gon P that induces A by extending every edge of P into a line. We prove that such a polygon always exists and can be found in O(nlogn) time. In fact, we show that every finite family of curves 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 C contains a simple cycle that visits every curve in C exactly once.

Original languageEnglish
Pages (from-to)861-878
Number of pages18
JournalComputational Geometry: Theory and Applications
Issue number7
StatePublished - 2013

Bibliographical note

Funding Information:
Research by Eyal Ackerman was supported by a fellowship from the Alexander von Humboldt Foundation . Research by Rom Pinchasi was supported by the Israeli Science Foundation (grant No. 938/06 ).


  • Inducing polygons
  • Line arrangement

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


Dive into the research topics of 'On inducing polygons and related problems'. Together they form a unique fingerprint.

Cite this