Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Computational Geometry: Theory and Applications
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces
SIAM Journal on Computing
High-dimensional computational geometry
High-dimensional computational geometry
Distributed similarity search in high dimensions using locality sensitive hashing
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
Approximate range searching: The absolute model
Computational Geometry: Theory and Applications
Approximate Halfspace Range Counting
SIAM Journal on Computing
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Applying standard dimensionality reduction techniques, we show how to perform approximate range searching in higher dimension while avoiding the curse of dimensionality. Given n points in a unit ball in R^d, an approximate halfspace range query counts (or reports) the points in a query halfspace; the qualifier ''approximate'' indicates that points within distance @e of the boundary of the halfspace might be misclassified. Allowing errors near the boundary has a dramatic effect on the complexity of the problem. We give a solution with O@?(d/@e^2) query time and dn^O^(^@e^^^-^^^2^) storage. For an exact solution with comparable query time, one needs roughly @W(n^d) storage. In other words, an approximate answer to a range query lowers the storage requirement from exponential to polynomial. We generalize our solution to polytope/ball range searching.