**Assigned:**
Thursday, February 2, 2006

**Due:**
Wednesday, February 8, 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 13.14. Tree minimax result.
- Problem 13.30. Most vital arcs.
- Problem 13.34. Balanced Spanning Trees.
- Prove or disprove the following statement. Let G=(V,E) be a graph with non-negative edge
weights w, and let T be the minimum spanning tree. Let H be a graph formed from G by doubling each
of the edge weights. T is a minimum spanning tree of H.
- Consider the case where the edge weights are all integers in the range 1 to 10.
Explain how to implement Prim's algorithm so that it runs in linear time.

### Switch to:

cliff@ieor.columbia.edu