ESA 2009: Algorithms - ESA 2009 pp 47-58

# On Inducing Polygons and Related Problems

• Eyal Ackerman
• Rom Pinchasi
• Ludmila Scharf
• Marc Scherfenberg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5757)

## 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.

## Keywords

Intersection Point Base Line Simple Path Internal Vertex Simple Polygon
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## 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