Dynamic maintenance of maxima of 2-D point sets

This paper describes an efficient scheme for the dynamic maintenance of the set of maxima of a 2-d set of points. Using the fact that the maxima can be stored in a staircase structure, we use a technique in which we maintain approximations to the staircase structure. We first describe how to maintain the maxima in O(log n) time per insertion and deletion when there are n insertions and deletions. O(log n) is charged per change for reporting changes to the staircase structure which stores the maxima. O(n) space is used. We also show another scheme which requires a total of O(n log n + r) time when r maximal points are listed. We finally consider extensions to higher dimensions.