**Assigned:**
Thursday, March 23, 2006

**Due:**
Wednesday, March 29, 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 7.15. FIFO algorithm.
- Problem 7.14. Generic preflow-push.
- Problem 7.18. Note that the capacity scaling algorithm is slightly different, but related to the bit scaling algorithm and the maximum capacity path algorithm covered in class.
- Another variant of the prelfow-push algorithms is called "relabel-to-front". This algorithm
works like the FIFO algorithm, except that we maintain the list of active vertices in a different
way. Here the rule is that whenever we relabel a vertex it moves to the front of the list. We
always choose the vertex at the front of the list for a discharge operation. Note that this means that
if you are performing a discharge operation from node v, and v is relabeled, v then goes on the front of the list, and you call discharge on v again. Show that the relabel-to-front algorithm
runs in O(V
^{3}) time.
- Problem 7.29. Parametric maximum flow.

### Switch to:

cliff@ieor.columbia.edu