Reporting the crossing-free segments of a complete geometric graph

A complete geometric graph is a pair (S, E), where S = {p(1),......,p(n)} is a set of n points in general position on the Euclidean plane and E the set of all closed line segments whose endpoints are in S. A closed segment e(s, t) from p(s) to p(t) is crossing-free, if e(s, t) does not cross any segment in E. In this paper, we will propose an algorithm that reports all crossing-free segments of (S, E) in O(n(2)) time.