An optimal extension of the centerpoint theorem

Alon, 1992, Point selections and weak e-nets for convex hulls, Combin. Probab. Comput., 1, 189, 10.1017/S0963548300000225 B. Aronov, F. Aurenhammer, F. Hurtado, S. Langerman, D. Rappaport, S. Smorodinsky, C. Seara, Small weak epsilon nets, in: Proc. 17th Canadian Conference on Computational Geometry, 2005 B. Chazelle, H. Edelsbrunner, M. Grigni, L. Guibas, M. Sharir, E. Welzl, Improved bounds on weak eps-nets for convex sets, in: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, 1993, pp. 495–504 Clarkson, 1996, Approximating center points with iterative radon points, Int. J. Comput. Geom. Appl., 6, 357, 10.1142/S021819599600023X Danzer, 1986, On the solution of the problem of Gallai about circular discs in the Euclidean plane, Stud. Sci. Math. Hung., 21, 111 Haussler, 1987, ε-nets and simplex range queries, Discrete Comput. Geom., 2, 127, 10.1007/BF02187876 Miller, 1997, Separators for sphere-packings and nearest neighbor graphs, J. ACM, 44, 1, 10.1145/256292.256294 Matousek, 2002 F.F. Yao, A 3-space partition and its applications, in: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, 1983, pp. 258–263 G.L. Miller, S.-H. Teng, W.P. Thurston, S.A. Vavasis, Automatic mesh partitioning, in: Workshop on Sparse Matrix Computations: Graph Theory Issues and Algorithms, 1993 Donoho, 1994, Breakdown properties of location estimates based on halfspace depth and projected outlyingness, Ann. Statist., 20, 1803, 10.1214/aos/1176348890 Matousek, 2004, New constructions of weak epsilon-nets, Discrete Comput. Geom., 32, 195, 10.1007/s00454-004-1116-4 Pach, 1995