Efficient data structures for range searching on a grid
Journal of Algorithms
Two- and three-dimensional point location in rectangular subdivisions
Journal of Algorithms
Efficient 3-D range searching in external memory
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
The P-range tree: a new data structure for range searching in secondary memory
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Approximate data structures with applications
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Multidimensional divide-and-conquer
Communications of the ACM
Optimal static range reporting in one dimension
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
New data structures for orthogonal range searching
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Faster deterministic sorting and searching in linear space
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
On dynamic range reporting in one dimension
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
Fully Dynamic Orthogonal Range Reporting on RAM
SIAM Journal on Computing
Dynamic ordered sets with exponential search trees
Journal of the ACM (JACM)
On approximate halfspace range counting and relative epsilon-approximations
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
On approximate range counting and depth
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A data structure for multi-dimensional range reporting
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
On Approximating the Depth and Related Problems
SIAM Journal on Computing
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Space-Efficient and fast algorithms for multidimensional dominance reporting and counting
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Efficient range searching for categorical and plain data
ACM Transactions on Database Systems (TODS)
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We present new data structures for approximately counting the number of points in an orthogonal range. There is a deterministic linear space data structure that supports updates in O(1) time and approximates the number of elements in a 1-D range up to an additive term k 1/c in O(loglogU·loglogn) time, where k is the number of elements in the answer, U is the size of the universe and c is an arbitrary fixed constant. We can estimate the number of points in a two-dimensional orthogonal range up to an additive term k ρ in O(loglogU + (1/ρ)loglogn) time for any ρ 0. We can estimate the number of points in a three-dimensional orthogonal range up to an additive term k ρ in O(loglogU + (loglogn)3 + (3 v )loglogn) time for $v=\log \frac{1}{\rho}/\log \frac{3}{2}+2$.