Approximation Algorithms Part II (Coursera)

Upon completion, you will be able to recognize, when faced with a new combinatorial optimization problem, whether it is close to one of a few known basic problems, and will be able to design linear programming relaxations and use randomized rounding to attempt to solve your own problem. The course content and in particular the homework is of a theoretical nature without any programming assignments.

This is the second of a two-part course on Approximation Algorithms, this is the continuation of Approximation algorithms, Part 1

Syllabus

WEEK 1

Linear Programming Duality

This module does not study any specific combinatorial optimization problem. Instead, it introduces a central feature of linear programming, duality.

WEEK 2

Steiner Forest and Primal-Dual Approximation Algorithms

This module uses linear programming duality to design an algorithm for another basic problem, the Steiner forest problem.

WEEK 3

Facility Location and Primal-Dual Approximation Algorithms

This module continues teaching algorithmic applications of linear programming duality by applying it to another basic problem, the facility location problem.

WEEK 4

Maximum Cut and Semi-Definite Programming

We introduce a generalization of linear programming, semi-definite programming.This module uses semi-definite programming to design an approximation algorithm for another basic problem, the maximum cut problem.