This is a graduate-level course in combinatorial optimization with a focus on polyhedral characterizations. In the first part of the course, we will cover some classical results in combinatorial optimization: algorithms and polyhedral characterizations for matchings, spanning trees, matroids, and submodular functions. In the second part, we will cover some more recent work that builds upon these techniques - approximation algorithms using the primal-dual scheme, iterated rounding and dependent randomized rounding. Applications will include allocation in combinatorial auctions, network design, and variants of the traveling salesman problem.
Students should know basic computation theory and the material of CS 261; in particular the fundamentals of linear programming, approximation algorithms and the notion of NP-completeness.
There will be bi-weekly homeworks which constitute 50%. A take-home final exam will count for the remaining 50%.
In addition, students will be asked to scribe notes in LaTeX. Writing up one lecture allows you to skip one homework. Additional material: