Download COMP 4045 - Computational Geometry

COMP 4045 - Computational Geometry Assignment 3
1. Prove that for any n > 3 there is a set of n sites in the plane such that one of the
Voronoi region has n-1 vertices. (Exercises 7.1).
2. Let P be a set of n points in the plane. Give an O(nlogn) time algorithm to find two
points in P that are closest together. (Exercises 7.10).
a) Design an algorithm;
b) Prove its correctness;
c) Show its time complexity.
3. The idea of Voronoi Diagram can be further extended. For instance, k nearest points is
required in some cases instead of the nearest one. This problem is known as “order-k
Voronoi Diagram”. (please make clear acknowledgement of any previous work)
a) Design an algorithm;
b) Prove its correctness;
c) Show its time and storage complexity.