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Proceedings of 37th Conference on Foundations of Computer Science (1996)
Burlington, VT
Oct. 14, 1996 to Oct. 16, 1996
ISBN: 0-8186-7594-2
pp: 472
J. Erickson , Comput. Sci. Div., California Univ., Berkeley, CA, USA
ABSTRACT
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.
INDEX TERMS
computational complexity; halfspace emptiness; lower bounds; hyperplanes; points; polylogarithmic factors; partitioning algorithms; query region; polyhedron; facets
CITATION

J. Erickson, "New lower bounds for halfspace emptiness," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 472.
doi:10.1109/SFCS.1996.548506
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