Abstract
Attempts to generalize Helly’s theorem to sets of lines intersecting convex sets led to a series of results relating the geometry of a family of sets in ℝd to the structure of the space of lines intersecting all of its members. We review recent progress in the special case of disjoint Euclidean balls in ℝd, more precisely the inter-related notions of cone of directions, geometric permutations and Helly-type theorems, and discuss some algorithmic applications.
Keywords
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Goaoc, X. (2009). Some Discrete Properties of the Space of Line Transversals to Disjoint Balls. In: Emiris, I., Sottile, F., Theobald, T. (eds) Nonlinear Computational Geometry. The IMA Volumes in Mathematics and its Applications, vol 151. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0999-2_3
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