KTH / CSC / Theory Group / Tobias Mömke / FDD3402 Combinatorial Optimization

Date | Time | Place | Section | Topic |
---|---|---|---|---|

Wednesday, 15 February 2012 | 10:15 to 12:00 | Room 1537 | Polyhedral Combinatorics | Introduction, Background in Polyhedra, LP Duality |

Monday, 20 February 2012 | 10:15 to 12:00 | Room 1635 | Polyhedral Combinatorics | Integer Programming Background, Totally Unimodular Matrices |

Monday, 27 February 2012 | 10:15 to 12:00 | Room 1635 | Polyhedral Combinatorics | Applications of Totally Unimodular Matrices |

Monday, 5 March 2012 | 10:15 to 12:00 | Room 1635 | Polyhedral Combinatorics | Total Dual Integrality, Matching Polytope |

Monday, 12 March 2012 | 10:15 to 12:00 | Room 1635 | Matroids | Introduction, Greedy Algorithm |

Monday, 19 March 2012 | 10:15 to 12:00 | Ringenhuset, Room 523 | Matroids | Examples of Matroids, Duality |

Monday, 26 March 2012 | 10:15 to 12:00 | Room 1535 |
Matroids | Characterizations, Independent Set Polytope, Matroid Intersection |

Wednesday, 4 April 2012 | 10:15 to 12:00 | Room 1635 | Matroids | Application of Intersection Theorem, Matroid Partition, Intersection of Independent Set Polytopes |

Wednesday, 11 April 2012 | 10:15 to 12:00 | Room 1635 | Expanders | Introduction, Applications |

Monday, 16 April 2012 | 10:15 to 12:00 | Room 1635 | Expanders | Spectral Expansion, Mixing Lemma, Ramanujan Graphs |

Monday, 23 April 2012 | 10:15 to 12:00 | Room 1635 | Expanders | Zig-zag Product, SL=L |

Monday, 30 April 2012 | 10:15 to 12:00 | Room 1635 | Expanders | Lossless expanders and conductors |

The lectures will be given weekly in 2-hour lectures for 12 weeks.

The problem sets are distributed via email.

After the course, the students should

- know basic concepts from polyhedral combinatorics
- be able to recognize several types efficiently solvable problems based on polyhedral techniques and matroids
- be able to understand techniques from combinatorial optimization used in research papers
- have an enhanced base of techniques to approach open algorithmic problems

The course aims to give a foundation of advanced techniques that lead to efficient exact algorithms. After an introduction to fundamental polyhedral concepts such as integer polyhedra and their connection to totally unimodular matrices, the course focuses on matroids and their connection to greedy algorithms. The last part of the course introduces expander graphs from a combinatorial optimization point of view.

The course is mainly targeted to graduate students at KTH in computer science and mathematics, but also open for advanced undergraduate students.

The course is selfcontained, but it is beneficial to have basic knowledge of optimization problems and in particular linear programming as it was provided, for instance, in the course DD3390 "Approximation Algorithms" given by Ola Svensson in 2010.

Alexander Schrijver: Combinatorial Optimization: Polyhedra and Efficiency

Bernhard Korte and Jens Vygen: Combinatorial Optimization: Theory and Algorithms

S. Hoory, N. Linial, A. Wigderson: Expander Graphs and their Applications , Bull. Amer. Math Soc., 43, pp 439--561, 2006.

Combinatorial Optimization Part
Expander Part
Further Background on Spectral Graph Theory

Omer Reingold, Salil Vadhan, Avi Wigderson: Entropy Waves, the Zig-Zag Graph Product, and New Constant-Degree Expanders and Extractors , Electronic Colloquium on Computational Complexity (ECCC) 8(18): (2001) (Conference version: FOCS 2000)