Abstract
We give a data structure that allows arbitrary insertions and deletions on a planar point set P and supports basic queries on the convex hull of P, such as membership and tangent-finding. Updates take O(log{1+eps}n) amortized time and queries take O(log n) time each, where n is the maximum size of P and eps is any fixed positive constant. For some advanced queries such as bridge-finding, both our bounds increase to O(log{3/2}n). The only previous fully dynamic solution was by Overmars and van Leeuwen from 1981 and required O(log2 n) time per update.