Approximation Algorithms Part II

Approximation algorithms, Part 2 This is the continuation of Approximation algorithms, Part 1. Here you will learn linear programming duality applied to the design of some approximation algorithms, and semidefinite programming applied to Maxcut. By taking the two parts of this course, you will be exposed to a range of problems at the foundations of theoretical computer science, and to powerful design and analysis techniques. 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.

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