This paper proves an O(m2/3n2/3 + m + n) upper bound on the number of incidences between m points and n hyperplanes in four dimensions, assuming all points lie on one side of each hyperplane and the points and hyperplanes satisfy certain natural general position conditions. This result has application to various three-dimensional combinatorial distance problems. For example, it implies the same upper bound for the number of bichromatic minimum distance pairs in a set of m blue and n red points in three-dimensional space. This improves the best previous bound for this problem.
CITATION STYLE
Edelsbrunner, H., & Sharir, M. (1990). A hyperplane incidence problem with applications to counting distances. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 450 LNCS, pp. 421–428). Springer Verlag. https://doi.org/10.1007/3-540-52921-7_91
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