The primal–dual method for approximation algorithms

In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to NP-hard problems in combinatorial optimization. Because of parallels with the primal–dual method commonly used in combinatorial optimization, we call it the primal–dual method for approximation algorithms. We show how this technique can be used to derive approximation algorithms for a number of different problems, including network design problems, feedback vertex set problems, and facility location problems.