Achieving Spatial Adaptivity while Finding Approximate Nearest Neighbors
نویسندگان
چکیده
We present the first spatially adaptive data structure that answers approximate nearest neighbor (ANN) queries to points that reside in a geometric space of any constant dimension. The running time for a query q is O(lg δ(p, q)), where p is the result of the preceding query and δ(p, q) is the number of input points in a reasonably sized box containing p and q. Moreover, the data structure has O(n) size and requires O(n lg n) preprocessing time, where n is the number of points in the data structure. The constant factors in the above bounds depend on the dimension d. For points in d dimensions, the Ltnorm approximation ratio is O(d 1 t ). Our results use the RAM model with words of size Θ(lg n).
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