New Results on Dynamic Planar Point Location

A point location scheme is presented for an n-veriet dynamic planar subdivision whose underlying graph is only required to be connected. The scheme uses O(n) space, yields an O(log2 n) query time and an O(1ogn) update time. Insertion (resp. deleiion) of an arbitrary k-edge chain inside a region can be performed in O(klog(n+k)) (resp. O(k1ogn)) iime. The scheme is then ectended to speed up the insertion/deletion of a kedge monotone chain to O(log2nloglogn+k) time (or O(1ogn loglogn + k) iime for an oltemative model of input), but ai ihe ecpense of increasing the other time bounds slightly. All bounds are worst-case. Additional results include a generalizaiion to planar subdivisions consisting of algebraic segments of bounded degree and a persistent scheme for planar point location.