Window queries for intersecting objects, maximal points and approximations using coresets

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 R-d, d >= 2. Finally we present techniques to approximate window-aggregate queries for (1+epsilon)-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. (C) 2021 Elsevier B.V. All rights reserved.