Lecture 11

Learning objectives

After this class, you should be able to:

1. Given a problem, pose it as an integer linear program, give its relaxation, discretize the result to get an approximate solution to the problem, and derive its approximation factor.

Reading assignment

1. Chapter 14, section 14.1.
2. Section 12.1.

Exercises and review questions

• Questions on current lecture's material
  1. Give an integer linear program for the bin packing problem (chapter 9) and then give its relaxation. How will you discretize the result of the relaxation to get a feasible solution for the original problem? Can you derive an approximation factor?

• Questions on next lecture's material
  1. Give the dual of the relaxed version of the set cover linear program, and give the complementary slackness conditions for it.