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arXiv · 1809.10078

Convex partial transversals of planar regions

Vahideh Keikha·Mees van de Kerkhof·Marc van Kreveld·Irina Kostitsyna·Maarten Löffler·Frank Staals·Jérôme Urhausen·Jordi L. Vermeulen·Lionov Wiratma
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Abstract

We consider the problem of testing, for a given set of planar regions $\cal R$ and an integer $k$, whether there exists a convex shape whose boundary intersects at least $k$ regions of $\cal R$. We provide a polynomial time algorithm for the case where the regions are disjoint line segments with a constant number of orientations. On the other hand, we show that the problem is NP-hard when the regions are intersecting axis-aligned rectangles or 3-oriented line segments. For several natural intermediate classes of shapes (arbitrary disjoint segments, intersecting 2-oriented segments) the problem remains open.

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Vahideh Keikha, Mees van de Kerkhof, Marc van Kreveld, Irina Kostitsyna, Maarten Löffler, Frank Staals, Jérôme Urhausen, Jordi L. Vermeulen, Lionov Wiratma. 2018-09-26. Convex partial transversals of planar regions. https://doi.org/10.4230/lipics.isaac.2018.187

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