New results on dynamic planar point location

Abstract

A point location scheme is presented for an n-vertex dynamic planar subdivision whose underlying graph is only required to be connected. The scheme uses O(n) space and yields an O(log/sup 2/n) query time and an O(log n) update time. Insertion (respectively, deletion) of an arbitrary k-edge chain inside a region can be performed in O(k log(n+k)) (respectively, O(k log n)) time. The scheme is then extended to speed up the insertion/deletion of a k-edge monotone chain to O(log/sup 2/n log log n+k) time (or O(log n log log n+k) time for an alternative model of input), but at the expense of increasing the other time bounds slightly. All bounds are worst case. Additional results include a generalization to planar subdivisions consisting of algebraic segments of bounded degree and a persistent scheme for planar point location.<>