Aller au menu Aller au contenu
Une voie, plusieurs choix
Informatique et Mathématiques appliquées
Une voie, plusieurs choix

> Formation > Cursus ingénieur

Combinatorial optimization - 4MMOC6

A+Augmenter la taille du texteA-Réduire la taille du texteImprimer le documentEnvoyer cette page par mail Partagez cet article Facebook Twitter Linked In Google+ Viadeo
  • Number of hours

    • Lectures : 16.5
    • Tutorials : 16.5
    ECTS : 3.0

Goals

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.

Contact Zoltan SZIGETI

Content

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



Prerequisites

Linear programming (useful), elementary graph theory, seen in first year operations research course.

Tests

Written exam (3 h) (E)



N1=E1
N2=E2

Additional Information

Curriculum->Math. Modelling, Image & Simulation->Semester 7

Bibliography

Linear programming by Vacek Chvatal, (editeur Freeman)
Network flows by Ahuja, Magnati and Orlin (editeur Prentice Hall)

A+Augmenter la taille du texteA-Réduire la taille du texteImprimer le documentEnvoyer cette page par mail Partagez cet article Facebook Twitter Linked In Google+ Viadeo

Date of update January 15, 2017

Grenoble INP Institut d'ingénierie Univ. Grenoble Alpes