Constructing higher-dimensional convex hulls at logarithmic cost per face

We exhibit a new approach for dealing with higher dimensional convex hull problems, such as enumerating all facets of the convex hull of a finite point set or constructing the facial lattice of such a convex hull. For fixed dimensions our new algorithms have worst case time complexity O(m 2 -tFlogm), where m is the size of the input point set and F is the size of the output produced. Such a dependence on the output size is desirable since F can range between ~(1) and O(mld/2|). Our time bound is an improvement over the best previously achieved bounds for a large range of values of F. The main tool in our new approach is the notion of a straight line shelling of a polytope.