Problem 2 (Simple Polygon) 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 Graham's scan.) Problem 2 (Simple Polygon) 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 Graham's scan.)