**Assigned:**
Thursday, February 23, 2006

**Due:**
Wednesday, March 1, 2006

## General Instructions

- Please review the
course information.
- 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.
- Numbered problems are all from the textbook
* Network Flows *.

## Problems

- Problem 6.28. Maximum flows and minimum cuts.
- Problem 6.38. Submodularity of cuts.
- Problem 6.46. Matrix covering.
- Problem 6.40. Converting non-integer flows to integer flows.
- 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.
- Derive the maximum-flow minimum-cut theorem using linear programming
duality.

### Switch to:

cliff@ieor.columbia.edu