A randomized algorithm for closest-point queries
SIAM Journal on Computing
Vector quantization and signal compression
Vector quantization and signal compression
Point location in arrangements of hyperplanes
Information and Computation
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
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Dimensionality reduction techniques for proximity problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Optimal Expected-Time Algorithms for Closest Point Problems
ACM Transactions on Mathematical Software (TOMS)
Information Retrieval
Nearest Neighbors Can Be Found Efficiently If the Dimension Is Small Relative to the Input Size
ICDT '03 Proceedings of the 9th International Conference on Database Theory
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We present an algorithm for solving the nearest neighbor problem with respect to $L_{\infty}$-distance. It requires no preprocessing and storage only for the point set $P$. Its average runtime assuming that the set $P$ of $n$ points is drawn randomly from the unit cube $[0,1]^{d}$ under uniform distribution is essentially $\Theta (nd/ln\; n)$ thereby improving the brute-force method by a factor of $\Theta (1/ln\; n)$. Several generalizations of the method are also presented, in particular to other “well-behaved” probability distributions and to the important problem of finding the $k$ nearest neighbors to a query point.