Lecture 1

Learning objectives

After this class, you should be able to:

1. Describe the course policies, grading criteria, and your responsibilities.
2. Write a formal proof by induction.

Reading assignment

1. Read the syllabus and class notes.
2. CLR: Chapter 35, page 1022 and page 1024.

Exercises and review questions

• Questions on current lecture's material
  1. How many homework assignments will you have in this course?
  2. How many programming assignments will you have in this course?
  3. Will you be graded on class participation in this course?
  4. What will your grade be if you obtain a total score of 85% and an exam average of 50%?
  5. Consider a binary tree in which each node has either two children, or no children. Prove by induction that the number of leaf nodes in such a tree with n nodes is (n+1)/2. Please submit a hardcopy of your proof to me at the begining of the next lecture, if you want feedback from me.

• Questions on next lecture's material
  1. Suppose that an approximation algorithm for some maximization problem yields a solution that is at least as large as 0.8 OPT, where OPT is the value of the optimal solution. Give a good lower bound on the approximation ratio of this algorithm.
  2. Find a vertex cover of size three for the graph in figure 22.1 (page 528).