**Assigned:**
Thursday, February 17, 2011

**Due:**
Thursday, February 24, 2011

## 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
- Show how to find a maximum flow in a network via a sequence of
at most m augmenting paths. (Hint: you will need to more than start with
a zero flow and augment m times. You only need to eventually return at most m paths that, when augmented on in sequence lead to a maximum flow).
- Problem 6.38. Submodularity of cuts.

### Switch to:

cliff@ieor.columbia.edu