Dynamic Planar Convex Hull Operations in Near-Logarithmic Amortized Time

We give a data structure that allows arbitrary insertions and Adeletions on a planar point set P and supports basic queries on the convex hull of P, such as Amembership and tangent-finding. Updates take O(log^1+E n) amortized time and queries take O(log n) Atime each, where n is the maximum size of P and E is any fixed positive constant. For some Aadvanced queries such as bridge-finding, both our bounds increase to O(log^3/2 n). The only Aprevious fully dynamic Asolution was by Overmars and van Leeuwen from 1981 and required O(log^2 n) time per Aupdate and O(log n) time per query.