How hard is half-space range searching?
- Hervé BrönnimannAffiliated withDepartment of Computer Science, Princeton University
- , Bernard ChazelleAffiliated withDepartment of Computer Science, Princeton University
- , János PachAffiliated withDepartment of Computer Science, City College, C.U.N.Y.Courant Institute, N.Y.U.
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Although the bound is unlikely to be optimal, it falls reasonably close to the recent upper bound ofO(n/m 1/d ) established by Matoušek. We also show that it is possible to devise a sequence ofn inserts and half-space range queries that require a total time ofn 2-O(1/d) . Our results imply the first nontrivial lower bounds for spherical range searching in any fixed dimension. For example, they show that, with linear storage, circular range queries in the plane require Ω(n 1/3) time (modulo a logarithmic factor).
- How hard is half-space range searching?
Discrete & Computational Geometry
Volume 10, Issue 2 , pp 143-155
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- Springer New York
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- 1. Department of Computer Science, Princeton University, 35 Olden Street, 08544-2087, Princeton, NJ, USA
- 2. Department of Computer Science, City College, C.U.N.Y., 10031, New York, NY, USA
- 3. Courant Institute, N.Y.U., 251 Mercer Street, 10012, New York, NY, USA