Lecture 20

Learning objectives

After this class, you should be able to:

1. Given a DAG, topologically sort it.
2. Prove the correctness of the algorithm we discussed for topological sorting and give its time complexity.
3. Given a directed graph, find its strongly connected components.
4. Prove the correctness of the algorithm we discussed for finding strongly connected components and give its time complexity.
5. Given related graph problems, give algorithms to solve them, prove their correctness, and derive their time complexities.
6. Given incorrect algorithms for similar problems, give counterexamples to disprove them.

Reading assignment

1. CLR: Sections 22.4-22.5.
2. CLR: Chapter 23, pages 624-625.

Exercises and review questions

• Questions on current lecture's material
  1. Exercise 22.4-3.
  2. Exercise 22.5-2.

• Questions on next lecture's material
  1. (Post your solution on the discussion board) Give a graph with 5 vertices, and a spanning tree for it. (You need not assign weights to the edges.)