MA053 Matroid theory and combinatorial optimization

Faculty of Informatics
Spring 2008
Extent and Intensity
2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Timetable
Mon 13:00–15:50 B411
Prerequisites
Graph theory MA010, Linear algebra (ANY).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 50 student(s).
Current registration and enrolment status: enrolled: 0/50, only registered: 0/50, only registered with preference (fields directly associated with the programme): 0/50
fields of study / plans the course is directly associated with
there are 20 fields of study the course is directly associated with, display
Course objectives
The aim of this advanced subject is to introduce students to the basic and selected advanced concepts of matroid theory and its connections to combinatorial optimization. Roughly saying, matroids present an algebraic/geometric generalization of graphs, and everybody should know their connection with the greedy algorithm. However, matroid theory includes much more interesting topic and this subject touches many of them, including some cutting edge development in the recent years. At the end, students should: understand basic principles of matroid theory including applications in optimization; and be able to continue with some scientific work in this area if they choose to.
Syllabus
  • What is a matroid, relations to graphs and to linear algebra.
  • Matroid representations, finite fields. Duality and minors.
  • Matroids and the greedy algorithm.
  • Totally unimodular matrices and regular matroids. Seymour's decomposition.
  • Matroids and polyhedra, matroid intersection, Edmond's algorithm.
  • Excluded minors for matroid representability, Rota's conjecture.
  • Towards "matroid minor theory".
Literature
  • OXLEY, James G. Matroid theory. 1st pub. Oxford: Oxford University Press, 1997, xi, 532. ISBN 0198535635. info
Teaching methods
This is an advanced theoretical course, taught in English, and conducted quite informally (a seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/AMT.html
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