# IEOR 6614, Spring 2011 : Homework 4

Assigned: Thursday, February 10, 2011
Due: Thursday, February 17, 2011

## 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. 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).

2. Problem 5.38. Minimum length cycles.
3. Problem 5.46. Negative Cycles.
4. Give an O(nm) time algorithm that actually outputs the minimum mean cycle of a graph.
5. Problem 5.50. Minimum mean cycle example.

### Switch to:

cliff@ieor.columbia.edu