Abstract
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 for line segments, triangles and convex c-gons. We also present data structures to count points on maximal layer, k-dominated and k-dominant points for some fixed integer k, and to decide whether a given point belongs to a maximal layer for a sequence of points in Rd, d≥2. Finally we present techniques to approximate window-aggregate queries for (1+ε)-approximations for various geometric measures such as diameter, width, radius of a minimum enclosing ball, volume of the smallest bounding box, and the cost of ℓ-center clustering (ℓ≥2) for a set of points using coresets. All data structures presented in this paper answer queries in polylogarithmic time and use subquadratic space.
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