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}
}
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
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