Range-Aggregate Queries Involving Geometric Aggregation Operations

In this paper we consider range-aggregate query problems wherein we wish to preprocess a set S of geometric objects such that given a query orthogonal range q, a certain aggregation function on the objects S′ = S ∩ q can be answered efficiently. Range-aggregate version of point enclosure queries, 1-d segment intersection, 2-d orthogonal segment intersection (with/without distance constraint) are revisited and we improve the existing results for these problems. We also provide semidynamic (insertions) solutions to some of these problems. This paper is the first attempt to provide dynamic solutions to problems involving geometric aggregation operations.