# Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space

@article{HarPeled2012DownTR, title={Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space}, author={Sariel Har-Peled and Nirman Kumar}, journal={2012 IEEE 53rd Annual Symposium on Foundations of Computer Science}, year={2012}, pages={430-439} }

For a set of n points in Rd, and parameters k and e, we present a data structure that answers (1 + e)-approximate k nearest neighbor queries in logarithmic time. Surprisingly, the space used by the data-structure is Õ(n/k), that is, the space used is sub linear in the input size if k is sufficiently large. Our approach provides a novel way to summarize geometric data, such that meaningful proximity queries on the data can be carried out using this sketch. Using this we provide a sub linear… Expand

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