Enumerating Empty and Surrounding Polygons

We are given a set S of n points in the Euclidean plane. assume that is general position. A simple polygon P an empty if each vertex point and every either outside or P. In this paper, we consider problem enumerating all polygons set. To design efficient enumeration algorithm, use reverse search by Avis Fukuda with child lists. propose algorithm enumerates O(n2 |ϵ(S) |)-time, where ϵ(S) S. Moreover, applying same idea to surrounding S, them O(n2)-delay, while known log n)-delay, such inside polygon.