Window Queries for Problems on Intersecting Objects and Maximal Points.

We present data structures that can answer window queries for a sequence of geometric objects, such as points, line segments, triangles and convex c-gons. We first present data structures to solve windowed intersection decision problems using line segments, triangles and convex c-gons. We also present data structures to count points on maximal layer, to decide whether a given point belongs to a maximal layer, and to count k-dominant points for a fixed integer k for a sequence of points in Rd, d >= 2. All data structures presented in this paper answer queries in polylogarithmic time and use subquadratic space.