FDD3402 Combinatorial Optimization 6.0 credits

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 integral 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.

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 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.

If the course is discontinued, students may request to be examined during the following two academic years.

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Per Austrin

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

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