COP 4531: Lecture 23

Learning objectives

After this class, you should be able to:

1. Explain the difference between optimization problems and decision problems.
2. Explain what a polynomial time reduction is.
3. Explain what the class NP is and relate it to polynomial time verfication.
4. Explain what NP-completeness is.
5. Given an optimization problem, create a decision version of the problem and show that the decision version can be solved in polynomial time if and only is the optimization version can be solved in polynomial time.
6. Given a problem, show that it is in NP.

Reading assignment

1. CLR: Sections 34.1-3.

Exercises and review questions

• Questions on current lecture's material
  1. Exercise 34.1-1.
  2. Problem 34.2-1.

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