COP 4531: Lecture 22

Learning objectives

After this class, you should be able to:

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

Reading assignment

1. CLR: Sections 22.4 - 22.5.
2. CLR: Chapter 2, pages 561-562.

Exercises and review questions

• Questions on current lecture's material
  1. Remove the edge (fg, h) in figure 22.9 c, and topologically sort the resulting graph.
  2. Exercise 22.5-2.
  3. Exercise 22.5-3.

• 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.)