Elsevier

Computational Geometry

Volume 46, Issue 7, October 2013, Pages 861-878
Computational Geometry

On inducing polygons and related problems

https://doi.org/10.1016/j.comgeo.2011.06.003Get rights and content
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Abstract

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.

Keywords

Inducing polygons
Line arrangement

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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).