**Assigned:**
Thursday, February 16, 2006

**Due:**
Wednesday, February 22, 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 4.10. Multiple-knapsack problem.
- Suppose that you have a graph that is not strongly connected.
Show that Johnson's algorithm for all-pairs shortest (Theorem 5.4 in AMO)
might no longer be correct. Then give a modification that ensures that
leads to a correct algorithm.
- Problem 5.51 and 5.52. Scaling for shortest paths. It would be helpful
to read Section 3.3.
- Problem 5.18. Reoptimizing shortest paths.

### Switch to:

cliff@ieor.columbia.edu