- 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*.

- 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).

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

cliff@ieor.columbia.edu