Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
J. Erickson , Comput. Sci. Div., California Univ., Berkeley, CA, USA
The author derives a lower bound of /spl Omega/(n/sup 4/3/) for the halfspace emptiness problem: given a set of n points and n hyperplanes in R/sup 5/, is every point above every hyperplane? This matches the best known upper bound to within polylogarithmic factors, and improves the previous best lower bound of /spl Omega/(nlogn). The lower bound applies to partitioning algorithms in which every query region is a polyhedron with a constant number of facets.
computational complexity; halfspace emptiness; lower bounds; hyperplanes; points; polylogarithmic factors; partitioning algorithms; query region; polyhedron; facets
J. Erickson, "New lower bounds for halfspace emptiness," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 472.