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In the first year operations research course we studied some optimization algorithms on graphs, namely the shortest path problem in some particular cases and the minimum spanning tree problem. In this course we will go ahead and see more such algorithms: maximum flow problem, min cost flow problems, maximum cardinality or weight matching problem, and shortest path problems in the general case. We will also see many nice min-max or max-min theorems. This course put an emphasis in modelling and in algorithmics.
1. Maximum flow in a network : Ford and Fulkerson algorithm, preflow algorithms
2. Min cost flow problem : flow simplex algorithm, primal dual algorithm.
3. Shortest path problems general algorithm and finding of negative length cycles..
4. Maximum matching algorithm. The Edmonds-Gallai theorem.
5. Modeling real world problems as flow problems.
6. Some min-max theorems arising from network flow problems
Linear programming (useful), elementary graph theory, seen in first year operations research course.
Linear programming by Vacek Chvatal, (editeur Freeman)
Network flows by Ahuja, Magnati and Orlin (editeur Prentice Hall)
Written exam (3 h) (E)