Dynamic planar convex hull operations in near-logarithmic amortized time

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(log11e n) amortized time and queries take O(log n) time each, where n is the maximum size of P and e is any fixed positive constant. For some advanced queries such as bridge-finding, both our bounds increase to O(log3/2 n). The only previous fully dynamic solution was by Overmars and van Leeuwen from 1981 and required O(log2 n) time per update and O(log n) time per query