A New Approach to the Dynamic Maintaince of Maximal Points in a Plane

A point Pi = (Xi' Yi) in the x-y plane is maximal if there is no point Pi = (Xl> Yi) such that xi> Xi and Yi > Yi. We present a simple data structure, a dynamic contour search tree, which contains all the points in the plane and maintains an embedded linked list of maximal points so that m maximal points are accessible in O(m) time. Our data structure dynamically maintains the set of points so that insertions take O(log n) time, a speedup of O(log n) over previous results, and deletions take O({log n )2) time.