We describe two widely used methods for the design and analysis of approximation algorithms, the primal-dual schema and the local ratio technique. We focus on the creation of both methods by revisiting two results by Bar-Yehuda and Even-the linear time primal-dual approximation algorithm for set cover, and its local ratio interpretation. We also follow the evolution of the two methods by discussing more recent studies. © Springer-Verlag Berlin Heidelberg 2006.
Bar-Yehuda, R., & Rawitz, D. (2006). A tale of two methods. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3895 LNCS, 196–217. https://doi.org/10.1007/11685654_9