TY - GEN

T1 - Stronger bounds for weak epsilon-nets in higher dimensions

AU - Rubin, Natan

N1 - Publisher Copyright:
© 2021 ACM.

PY - 2021/6/15

Y1 - 2021/6/15

N2 - Given a finite point set P in Rd, and >0 we say that N? Rd is a weak -net if it pierces every convex set K with |K P|? ? |P|. Let d? 3. We show that for any finite point set in Rd, and any ?>0, there exist a weak -net of cardinality O(1/?d-1/2+?), where ?>0 is an arbitrary small constant. This is the first improvement of the bound of O?(1/?d) that was obtained in 1993 by Chazelle, Edelsbrunner, Grigni, Guibas, Sharir, and Welzl for general point sets in dimension d? 3.

AB - Given a finite point set P in Rd, and >0 we say that N? Rd is a weak -net if it pierces every convex set K with |K P|? ? |P|. Let d? 3. We show that for any finite point set in Rd, and any ?>0, there exist a weak -net of cardinality O(1/?d-1/2+?), where ?>0 is an arbitrary small constant. This is the first improvement of the bound of O?(1/?d) that was obtained in 1993 by Chazelle, Edelsbrunner, Grigni, Guibas, Sharir, and Welzl for general point sets in dimension d? 3.

KW - computational geometry

KW - convex sets

KW - epsilon-nets

KW - selection theorems

UR - http://www.scopus.com/inward/record.url?scp=85108140212&partnerID=8YFLogxK

U2 - 10.1145/3406325.3451062

DO - 10.1145/3406325.3451062

M3 - Conference contribution

AN - SCOPUS:85108140212

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 989

EP - 1002

BT - STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Khuller, Samir

A2 - Williams, Virginia Vassilevska

PB - Association for Computing Machinery

T2 - 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021

Y2 - 21 June 2021 through 25 June 2021

ER -