A hyperplane Incidence problem with applications to counting distances

H. Edelsbrunner, M. Sharir, in:, Springer, 1990, pp. 419–428.

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Series Title
LNCS
Abstract
This paper proves an O(m 2/3 n 2/3+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.
Publishing Year
Date Published
1990-01-01
Acknowledgement
Research of the first author was supported by the National Science Foundation under grant CCR-8714565. Work of the second author was supported by Office of Naval Research Grants DCR-83-20085 and CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the NCRD — the Israeli National Council for Research and Development, and the Fund for Basic Research in Electronics, Computers and Communication administered by the Israeli Academy of Sciences.
Volume
450
Page
419 - 428
Conference
SIGAL: Special Interest Group on Algorithms, International Symposium on Algorithms
IST-REx-ID

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Edelsbrunner H, Sharir M. A hyperplane Incidence problem with applications to counting distances. In: Vol 450. Springer; 1990:419-428. doi:10.1007/3-540-52921-7_91
Edelsbrunner, H., & Sharir, M. (1990). A hyperplane Incidence problem with applications to counting distances (Vol. 450, pp. 419–428). Presented at the SIGAL:  Special Interest Group on Algorithms, International Symposium on Algorithms  , Springer. https://doi.org/10.1007/3-540-52921-7_91
Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances,” 450:419–28. Springer, 1990. https://doi.org/10.1007/3-540-52921-7_91.
H. Edelsbrunner and M. Sharir, “A hyperplane Incidence problem with applications to counting distances,” presented at the SIGAL:  Special Interest Group on Algorithms, International Symposium on Algorithms  , 1990, vol. 450, pp. 419–428.
Edelsbrunner H, Sharir M. 1990. A hyperplane Incidence problem with applications to counting distances. SIGAL:  Special Interest Group on Algorithms, International Symposium on Algorithms  , LNCS, vol. 450. 419–428.
Edelsbrunner, Herbert, and Micha Sharir. A Hyperplane Incidence Problem with Applications to Counting Distances. Vol. 450, Springer, 1990, pp. 419–28, doi:10.1007/3-540-52921-7_91.

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