Data Structures for Range-Aggregation over Categories

We solve instances of a general class of problems defined as follows: Preprocess a set S of possibly weighted colored geometric objects (e.g. points/orthogonal segments/rectangles) in IR, d ≥ 1 such that given a query orthogonal range q (e.g. hyperbox/point), we can report efficiently for each distinct color c of the points in S ∩ q, the tuple 〈 c, F(c) 〉 where F(c) is a function (e.g. weighted sum, bounding box etc.) of the objects of color c in q.