In this paper, we study top-[Formula: see text] aggregate (or group) nearest neighbor queries using the weighted Sum operator under the [Formula: see text] metric in the plane. Given a set [Formula: see text] of [Formula: see text] points, for any query consisting of a set [Formula: see text] of [Formula: see text] weighted points and an integer [Formula: see text], [Formula: see text], the top-[Formula: see text] aggregate nearest neighbor query asks for the [Formula: see text] points of [Formula: see text] whose aggregate distances to [Formula: see text] are the smallest, where the aggregate distance of each point [Formula: see text] of [Formula: see text] to [Formula: see text] is the sum of the weighted distances from [Formula: see text] to all points of [Formula: see text]. We build an [Formula: see text]-size data structure in [Formula: see text] time, such that each top-[Formula: see text] query can be answered in [Formula: see text] time. We also obtain other results with trade-off between preprocessing and query. Even for the special case where [Formula: see text], our results are better than the previously best work, which requires [Formula: see text] preprocessing time, [Formula: see text] space, and [Formula: see text] query time. In addition, for the one-dimensional version of this problem, our approach can build an [Formula: see text]-size data structure in [Formula: see text] time that can support [Formula: see text] time queries. Further, we extend our techniques to answer the top-[Formula: see text] aggregate farthest neighbor queries, with the same bounds.
On Top-k Weighted Sum Aggregate Nearest and Farthest Neighbors in the L1 Plane
