Problem 1 in the textbook Preparata & Shamos (p.148). Given N points in the plane, construct a simple polygon having them as its vertices. 1. Show that (N log N) is a lower bound to running time. 2. Design an algorithm to solve this problem. (Hint: Modify Grahams scan.)

Textbook: Computational Geometry: an Introduction, Springer-Verlag, 1993 (5th printing) by F.P. Preparata, and M.I. Shamos