Given an n-edge convex subdivision of the plane, is it possible to report its k intersections with a query line segment in O(k+ polylog(n)) time, using subquadratic storage? If the query is a plane and the input is a polytope with n vertices, can one achieve O(k+ polylog(n)) time with subcubie 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 of these questions is no, and we derive near-optimal solutions to these classical problems.
|Original language||English (US)|
|Number of pages||8|
|Journal||Conference Proceedings of the Annual ACM Symposium on Theory of Computing|
|State||Published - 2001|
|Event||33rd Annual ACM Symposium on Theory of Computing - Creta, Greece|
Duration: Jul 6 2001 → Jul 8 2001
All Science Journal Classification (ASJC) codes