@inproceedings{7a718453cb8340438e0de1d57cf02ed0,

title = "Points and triangles in the plane and halving planes in space",

abstract = "We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.",

author = "Boris Aronov and Guibas, {Leonidas J.} and Bernard Chazelle and Micha Sharir and Herbert Edelsbrunner and Rephael Wenger",

year = "1990",

doi = "10.1145/98524.98548",

language = "English (US)",

isbn = "0897913620",

series = "Proc Sixth Annu Symp Comput Geom",

publisher = "Publ by ACM",

pages = "112--115",

booktitle = "Proc Sixth Annu Symp Comput Geom",

note = "Proceedings of the Sixth Annual Symposium on Computational Geometry ; Conference date: 06-06-1990 Through 08-06-1990",

}