A NEW APPROACH TO THE DYNAMIC MAINTENANCE OF MAXIMAL POINTS IN A PLANE

A point pi=(xi, yi) in the x-y plane is maximal if there is no point pj=(xj, yj) such that xj>xi and yj>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. © 1990 Springer-Verlag New York Inc.