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We provide the first sub-linear sketching algorithm for estimating the planar Earth-Mover Distance with a constant approximation. For sets living in the two-dimensional grid [¿] 2 , we achieve space ¿ ¿ for approximation O(1/¿), for any desired 0 < ¿ < 1. Our sketch has immediate applications to the streaming and nearest neighbor search problems.
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Andoni et al. (2009) studied this question.