# Approximate near neighbors for general symmetric norms

@article{Andoni2017ApproximateNN, title={Approximate near neighbors for general symmetric norms}, author={Alexandr Andoni and Huy L. Nguyen and Aleksandar Nikolov and Ilya P. Razenshteyn and Erik Waingarten}, journal={Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing}, year={2017} }

We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every n, d = no(1), and every d-dimensional symmetric norm ||·||, there exists a data structure for (loglogn)-approximate nearest neighbor search over ||·|| for n-point datasets achieving no(1) query time and n1+o(1) space. The main technical ingredient of the algorithm is a low-distortion embedding of a symmetric norm into a low…

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