**Assigned:**
Thursday, February 19, 2009

**Due:**
Thursday, February 26, 2009

## 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 6.46. Matrix covering.
- Problem 6.40. Converting non-integer flows to integer flows.
- Problem 6.48. Ford-Fulkerson with irrational capacities
- 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.
- Problem 6.38. Submodularity of cuts.

### Switch to:

cliff@ieor.columbia.edu