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For a set of n points in ^d, and parameters k and , we present a data structure that answers (1+,k)- queries in logarithmic time. Surprisingly, the space used by the data-structure is (n /k); that is, the space used is sublinear 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 sublinear space data-structure that canarXiv:1111.2942v3 fatcat:4moay5csffgc5mvifsuxsyg7u4