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# Convex transversals

@article{Arkin2014ConvexT, title={Convex transversals}, author={Esther M. Arkin and Claudia Dieckmann and Christian Knauer and Joseph S. B. Mitchell and Valentin Polishchuk and Lena Schlipf and Shang Yang}, journal={Comput. Geom.}, year={2014}, volume={47}, pages={224-239} }

- Published 2014 in Comput. Geom.
DOI:10.1016/j.comgeo.2012.10.009

We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?” We prove that when the sets are segments in the plane, deciding existence of the convex stabber is NP-hard. The problem remains NP-hard if the sets are scaled copies of a convex polygon. We also show that in 3D the stabbing… CONTINUE READING