COP 4531: Lecture 25

Learning objectives

After this class, you should be able to:

1. Explain the linear programming based approximation algorithm for weighted vertex cover and prove its approximation ratio.
2. Given a graph with vertex weights, write an Integer Linear Program for solving the weighted vertex cover problem and give its relaxation. If given a solution to the relaxation, then give an approximate solution to the weighted vertex cover instance and give an a-posteriori bound on it approximation ratio.

Reading assignment

1. CLR: Chaper 35, section 35.4 (only the weighted vertex cover problem).

Exercises and review questions

• Questions on current lecture's material
  1. Give an Integer Linear Programming formulation for the graph in Figure 35.1, assuming that each vertex has weight 2 and then give its relaxation.

• Questions on next lecture's material
  1. None.