Computing partial sums in multidimensional arrays
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Lower bounds for orthogonal range searching: part II. The arithmetic model
Journal of the ACM (JACM)
Reporting points in halfspaces
Computational Geometry: Theory and Applications
ACM Computing Surveys (CSUR)
On linear-time deterministic algorithms for optimization problems in fixed dimension
Journal of Algorithms
Range searching and point location among fat objects
Journal of Algorithms
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Computational Geometry: Theory and Applications
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Space-time tradeoff for answering range queries (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Space-time tradeoffs for approximate spherical range counting
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the importance of idempotence
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Range Counting over Multidimensional Data Streams
Discrete & Computational Geometry
On approximate halfspace range counting and relative epsilon-approximations
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Approximate range searching in higher dimension
Computational Geometry: Theory and Applications
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Approximate range searching in the absolute error model
Approximate range searching in the absolute error model
The Effect of Corners on the Complexity of Approximate Range Searching
Discrete & Computational Geometry
On Approximate Range Counting and Depth
Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Enclosing weighted points with an almost-unit ball
Information Processing Letters
Approximation algorithm for the kinetic robust K-center problem
Computational Geometry: Theory and Applications
Tight lower bounds for halfspace range searching
Proceedings of the twenty-sixth annual symposium on Computational geometry
A unified approach to approximate proximity searching
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximate static and continuous range search in mobile navigation
Proceedings of the 5th International Conference on Ubiquitous Information Management and Communication
Efficient robust digital hyperplane fitting with bounded error
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Semialgebraic Range Reporting and Emptiness Searching with Applications
SIAM Journal on Computing
Efficient robust digital annulus fitting with bounded error
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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Range searching is a well known problem in the area of geometric data structures. We consider this problem in the context of approximation, where an approximation parameter @e0 is provided. Most prior work on this problem has focused on the case of relative errors, where each range shape R is bounded, and points within distance @e@?diam(R) of the range's boundary may or may not be included. We consider a different approximation model, called the absolute model, in which points within distance @e of the range's boundary may or may not be included, regardless of the diameter of the range. We consider range spaces consisting of halfspaces, Euclidean balls, simplices, axis-aligned rectangles, and general convex bodies. We consider a variety of problem formulations, including range searching under general commutative semigroups, idempotent semigroups, groups, and range emptiness. We show how idempotence can be used to improve not only approximate, but also exact halfspace range searching. Our data structures are much simpler than both their exact and relative model counterparts, and so are amenable to efficient implementation.