Optimal Data-Dependent Hashing for Approximate Near Neighbors

@article{Andoni2015OptimalDH,
  title={Optimal Data-Dependent Hashing for Approximate Near Neighbors},
  author={Alexandr Andoni and Ilya P. Razenshteyn},
  journal={Proceedings of the forty-seventh annual ACM symposium on Theory of Computing},
  year={2015}
}
We show an optimal data-dependent hashing scheme for the approximate near neighbor problem. For an n-point dataset in a d-dimensional space our data structure achieves query time O(d ⋅ nρ+o(1)) and space O(n1+ρ+o(1) + d ⋅ n), where ρ=1/(2c2-1) for the Euclidean space and approximation c>1. For the Hamming space, we obtain an exponent of ρ=1/(2c-1). Our result completes the direction set forth in (Andoni, Indyk, Nguyen, Razenshteyn 2014) who gave a proof-of-concept that data-dependent hashing… Expand
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