Primal Dividing and Dual Pruning : Output - Sensitive

In this paper, we give an algorithm for output-sensitive construction of an f-face convex hull of a set of n points in general position in E 4. Our algorithm runs in O((n + f)log 2 f) time and uses O(n + f) space. This is the rst algorithm within a polylogarithmic factor of optimal O(n log f + f) time over the whole range of f. By a standard lifting map, we obtain output-sensitive algorithms for the Voronoi diagram or Delaunay triangulation in E 3 and for the portion of a Voronoi diagram that is clipped to a convex polytope. Our approach simpliies the \ultimate convex hull algorithm" of Kirkpatrick and Seidel in E 2 and also leads to improved output-sensitive results on constructing convex hulls in E d for any even constant d > 4.