Lecture 37

Learning objectives

After this class, you should be able to:

1. Given a DAG, show the steps in topologically sorting the vertices using the O(|V| + |E|) time algorithm.
2. Give applications for topological sort.
3. Given a graph and a source vertex, show the steps in finding unweighted shortest paths from the source to all other vertices.
4. Give an application for the unweighted shortest path problem.
5. Given a graph algorithm, choose a suitable data structure to represent the graph and analyze the time and space requirements.

Reading assignment

1. Sections 9.2, 9.3.1.
2. Lecture: Graphs.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Topologically sort the DAG in figure 9.79 using the O(|V| + |E|) algorithm.
  2. Ignore the weights on the edges and find the shortest paths between vertex s and all other vertices in figure 9.79.
  3. Would you use an adjancency matrix or an adjaceny list to represent a graph with the better topological sort algorithm? Justify your answer based on the time and space requirements with each choice.
  4. Give practical applications for topologocal sort and unweighted shortest path. Post your answer on the discussion board.

• Questions on next lecture's material
  1. Start preparing for the final exam. Look at the finals review and post any questions that you would like answered on the discussion board.

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Last modified: 6 Dec 2011