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We start with a review of the pervasiveness of the nearest neighbor searchproblem and techniques used to solve it along with some experimental results.In the second chapter, we show reductions between two different classes of geo-metric proximity problems: the nearest neighbor problems to solve the Euclideanminimum spanning tree problem and the farthest neighbor problems to solve thek-centers problem. In the third chapter, we unify spatial partitioning treesun- der one framework the meta-tree. Finally, we propose a dual tree algorithmfor Bichromatic Closest Pair and measure the complexity of batch nearestneighbor search.

Aren't we all nearest neighbors: Spatial trees, high dimensional reductions and batch nearest neighbor search