Lower bounds for high dimensional nearest neighbor search and related problems

The cw.w of dimensionality describes the phenomenon whereby (in spite of extensive and continuing research) for various geometric search problems we only have algorithms with performance that grows exponentially in the dimension. Recent results But must the exact nearest neighbor search problem suffer this curse? We provide some evidence in support of the curse. Specifically we investigate the exact nearest neighbor search problem and the related problem of exact partial match within the asymmetric communication model first used by Miltersen 36 to study data structure problems. We derive non-trivial asymptotic lower bounds for the exact problem that stand in contrast to known algorithms for approximate nearest neighbor search.