Maintaining maxima under boundary updates

Given a set of point P is an element of R-2, we consider the well-known maxima problem, consisting of reporting the maxima (not dominated) points of P, in the dynamic setting of boundary updates. In this setting we allow insertions and deletions of points at the extremities of P: this permits to move a resizable vertical window on the point set. We present a data structure capable of answering maxima queries in optimal O(k) worst case time, where k is the size of the answer. Moreover we show how to maintain the data structure under boundary updates operation in O(log n) time per update. This is the first technique in a dynamic setting capable of both performing update operations and answering maxima queries in optimal worst case time.