TY - CHAP
AB - 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. © Springer-Verlag Berlin Heidelberg 1990.
AU - Edelsbrunner, Herbert
AU - Sharir, Micha
ID - 3566
SN - 978-0897913850
T2 - Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift
TI - A hyperplane incidence problem with applications to counting distances
VL - 4
ER -