IEOR 6614, Spring 2006 : Homework 6

General Instructions

1. Please review the course information.
2. You must write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
3. Numbered problems are all from the textbook Network Flows .

Problems

1. Problem 6.28. Maximum flows and minimum cuts.
2. Problem 6.38. Submodularity of cuts.
3. Problem 6.46. Matrix covering.
4. Problem 6.40. Converting non-integer flows to integer flows.
5. In class, we showed that the shortest augmenting path algorithm for maximum flow performs O(nm) iterations. Give an example of a family of networks for which the shortest augmenting path algorithm performs X iterations, and try to make X as large as possible.
6. Derive the maximum-flow minimum-cut theorem using linear programming duality.

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