# 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

## 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.
Original language English 1809.10078v1 29 arXiv Published - 26 Sep 2018

• cs.CG

## Fingerprint

Dive into the research topics of 'Convex partial transversals of planar regions'. Together they form a unique fingerprint.