Algorithms for range-aggregate query problems involving geometric aggregation operations

Abstract

We consider variations of the standard orthogonal range searching motivated by applications in database querying and VLSI lay-out processing. In a generic instance of such a problem, called a range-aggregate query problem we wish to preprocess a set 5 of geometric objects such that given a query orthogonal range q, a certain intersection or proximity query on the objects of 5 intersected by q can be answered efficiently. Efficient solutions are provided for point enclosure queries, 1-d interval intersection, 2-d orthogonal segment intersection and 1- and 2-d closest pair problems in this framework. Although range-aggregate queries have been widely investigated in the past for aggregation functions like average, count, min, max, sum etc. we consider geometric aggregation operations in this paper. © Springer-Verlag Berlin Heidelberg 2005.