Convex partial transversals of planar regions
Computational Geometry
2018-09-27 v1
Abstract
We consider the problem of testing, for a given set of planar regions and an integer , whether there exists a convex shape whose boundary intersects at least regions of . 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.
Keywords
Cite
@article{arxiv.1809.10078,
title = {Convex partial transversals of planar regions},
author = {Vahideh Keikha and Mees van de Kerkhof and Marc van Kreveld and Irina Kostitsyna and Maarten Löffler and Frank Staals and Jérôme Urhausen and Jordi L. Vermeulen and Lionov Wiratma},
journal= {arXiv preprint arXiv:1809.10078},
year = {2018}
}