Duction from a Workload D a ; I a ; Q a to a Workload

The nearest neighbor search (NNS) problem is the following: Given a set of n pointsP = fp1; : : : ; png in some metric spaceX, preprocess P so as to efficiently answer queries which require finding a point in P closest to a query point q 2 X. The approximate nearest neighbor search (c-NNS) is a relaxation of NNS which allows to return any point within c times the distance to the nearest neighbor (called c-nearest neighbor). This problem is of major and growing importance to a variety of applications. In this paper, we give an algorithm for (4 log1+ log 4d + 3)-NNS algorithm in l d 1 withO(dn logn) storage andO(d logn) query time. In particular, this yields the first algorithm for O(1)-NNS for l1 with subexponential storage. The preprocessing time is linear in the size of the data structure. The algorithm can be also used (after simple modifications) to output the exact nearest neighbor in time bounded byO(d logn) plus the number of (4 log1+ log 4d + 3)-nearest neighbors of the query point. Building on this result, we also obtain an approximation algorithm for a general class of product met-