 
Summary: CRBTree: An Efficient Indexing Scheme for
RangeAggregate Queries ?
Sathish Govindarajan, Pankaj K. Agarwal, and Lars Arge
Department of Computer Science, Duke University, Durham, NC 27708
fgsat, pankaj, largeg@cs.duke.edu
Abstract. We propose a new indexing scheme, called the CRBtree, for effi
ciently answering rangeaggregate queries. The rangeaggregate problem is de
fined as follows: Given a set of weighted points in R d , compute the aggregate of
weights of points that lie inside a ddimensional query rectangle. In this paper
we focus on rangeCOUNT, SUM, AVG aggregates. First, we develop an indexing
scheme for answering twodimensional rangeCOUNT queries that uses O(N=B)
disk blocks and answers a query in O(log B N) I/Os, where N is the number of
input points and B is the disk block size. This is the first optimal index struc
ture for the 2D rangeCOUNT problem. The index can be extended to obtain a
nearlinearsize structure for answering rangeSUM queries using O(log B N)
I/Os. We also obtain similar bounds for rectangleintersection aggregate queries,
in which the input is a set of weighted rectangles and a query asks to compute
the aggregate of the weights of those input rectangles that overlap with the query
rectangle. This result immediately improves a recent result on temporalaggregate
queries. Our indexing scheme can be dynamized and extended to higher dimen
