Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}

In this paper, we report progress on answering the open problem presented by Pagh [11], who considered the nearest neighbor search without false negatives for the Hamming distance. We show new data structures for solving the c-approximate nearest neighbors problem without false negatives for Euclidean high dimensional space R. These data structures work for any c = ω( √ log logn), where n is the number of points in the input set, with poly-logarithmic query time and polynomial preprocessing time. This improves over the known algorithms, which require c to be Ω( √ d). This improvement is obtained by applying a sequence of reductions, which are interesting on their own. First, we reduce the problem to d instances of dimension logarithmic in n. Next, these instances are reduced to a number of c-approximate nearest neighbor search instances in ( R )L space equipped with metric m(x, y) = max1≤i≤L(‖xi − yi‖2). 1998 ACM Subject Classification F.2.2; G.3