On inducing polygons and related problems

Eyal Ackerman, Rom Pinchasi, Ludmila Scharf, Marc Scherfenberg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Bose et al. [1] asked whether for every simple arrangement of n lines in the plane there exists a simple n-gon P that induces 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 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 contains a simple cycle that visits every curve in exactly once.

Original languageEnglish
Title of host publicationAlgorithms - ESA 2009 - 17th Annual European Symposium, Proceedings
Number of pages12
StatePublished - 2009
Externally publishedYes
Event17th Annual European Symposium on Algorithms, ESA 2009 - Copenhagen, Denmark
Duration: 7 Sep 20099 Sep 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5757 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th Annual European Symposium on Algorithms, ESA 2009

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 ).

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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