Range searching in a set of line segments

Abstract

The range pearr.hi.ng (or windowing) problem asks for an accommodation of a set of objects such that those objects that lie (partially) In a given axis-parallel rectangle can be reported efficiently. He solve the range searching problem for a set of n non-intersecting, but possibly touching, line segments in the plane and give a data structure that allows for range queries in 0(k+ log2 n) time, where k is the number of reported answers. The structure is dynamic and allows for insertions and deletions of line segments in 0(log 2 n) time. The structure uses 0(n log n) storage. The related problem of moving the window (range) parallel to one of the coordinate-axes, determining the first line segment that will become visible or stops being visible, Is treated as well and similar bounds are obtained.