Learning objectives

After this class, you should be able to:

1. Define the following terms: bipartite graph, matching, maximal matching, and maximum matching.
2. Given a bipartite graph, formulate it as a network flow problem, and use the Edmonds-Karp algorithm to find a maximum matching.
3. Prove correctness of the algorithm we studied to determine a maximum matching in a bipartite graph, and show that its time complexity is O(VE) for a bipartite graph G = (V,E).

Reading assignment

1. CLR: Section 26.3.
2. CLR: Chapter 35, page 1022 and page 1024.

Exercises and review questions

• Questions on current lecture's material
  1. Give an example of a bipartitite graph and a maximal matching for it, such that the maximal matching is not a maximum matching.
  2. CLR: Exercise 26.3-1.
  3. CLR: Exercise 26.3-2.
  4. CLR: Exercise 26.3-3.
• 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).