On counting point-hyperplane incidences
نویسندگان
چکیده
منابع مشابه
On counting point-hyperplane incidences
In this paper we discuss three closely related problems on the incidence structure between n points and m hyperplanes in d-dimensional space: the maximal number of incidences if there are no big bipartite subconfigurations, a compressed representation for the incidence structure, and a lower bound for any algorithm that determines the number of incidences (counting version of Hopcroft’s problem...
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Let d and k be integers with 1 ≤ k ≤ d − 1. Let Λ be a d-dimensional lattice and let K be a d-dimensional compact convex body symmetric about the origin. We provide estimates for the minimum number of k-dimensional linear subspaces needed to cover all points in Λ ∩ K. In particular, our results imply that the minimum number of k-dimensional linear subspaces needed to cover the d-dimensional n ×...
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We show tha t m dist inct cells in an a r r angemen t of n planes in R a are bounded by O(m2/an + n 2) faces, which in turn yields a tight bound on the maximum number of facets bounding m cells in an arrangement of n hyperplanes in R a, for every d > 3. In addition, the method is extended to obtain tight bounds on the maximum number of faces on the boundary of all nonconvex cells in an arrangem...
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The number of external facets of a simple arrangement depends on its combinatorial type. A computation framework for counting the number of external facets is introduced and improved by exploiting the combinatorial structure of the set of sign vectors of the cells of the arrangement. 1 Background and introduction n hyperplanes in dimension d form a hyperplane arrangement. An hyperplane arrangem...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2003
ISSN: 0925-7721
DOI: 10.1016/s0925-7721(02)00127-x