Lecture 14

Learning objectives

After this class, you should be able to:

1. Define the MAX-SAT problem.
2. Given an instance of MAX-SAT, show how you can formulate it as an integer linear program.
3. Explain the two basic randomized approximate algorithms for the above problem, and their respective derandomizations.
4. Prove the correctness of the above algorithms, and derive the approximation factors for them.

Reading assignment

1. Chapter 16.

Exercises and review questions

• Questions on current lecture's material
  1. (Post your answer on the discussion board) Give an instance of MAX-SAT with at least four variables and at least four clauses, and give the integer linear program corresponding to this instance.
  2. Show that (1 - 1/k)k < 1/e, k > 1 .
  3. Show that 1 - (1-z/k)k > betak z, z in [0,1].
  4. (Post your answer on the discussion board) Give an application for MAX-SAT.

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