Lower bounds for intersection searching and fractional cascading in higher dimension

Bernard Chazelle, Ding Liu
2001 Proceedings of the thirty-third annual ACM symposium on Theory of computing - STOC '01  
Given an n-edge convex subdivision of the plane, is it possible to report its k intersections with a query line segment in Oðk þ polylogðnÞÞ time, using subquadratic storage? If the query is a plane and the input is a polytope with n vertices, can one achieve Oðk þ polylogðnÞÞ time with subcubic storage? Does any convex polytope have a boundary dominant Dobkin-Kirkpatrick hierarchy? Can fractional cascading be generalized to planar maps instead of linear lists? We prove that the answer to all
more » ... these questions is no, and we derive near-optimal solutions to these classical problems. r
doi:10.1145/380752.380818 dblp:conf/stoc/ChazelleL01 fatcat:qr6xnf23jzfmdnglqzddx46bpa