# IEOR 6614, Spring 2009 : Homework 4

Assigned: Thursday, February 12, 2009
Due: Thursday, February 19, 2009

## General Instructions

1. Please review the course information.
2. 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.
3. Numbered problems are all from the textbook Network Flows .

## Problems

1. Problem 5.18. Reoptimizing shortest paths.
2. We define a shortest path algorithm to be oblivious if given a graph G=(V,E), with vertices numbered 1..n, it decides to a execute a series of relax statements based only the values n = |V| and m = |E|, and not based on the particular structure of the graph. For example, Bellman-Ford algorithm is oblivious, but Dijkstra's algorithm is not.

Prove the following statement: Any oblivious algorithm that correctly computes single source shortest paths for all graphs G, must have a worst-case running time of Ω(nm).

3. Problem 5.40. Sensitivity analysis for shortest paths.
4. Problem 5.50. Minimum mean cycle example.
5. Problem 6.2. Staff scheduling.

### Switch to:

cliff@ieor.columbia.edu