As noted in Section 12.3, the primal-dual schema is the method of choice for designing approximation algorithms since it yields combinatorial algorithms with good approximation factors and good running times. We will first present the central ideas behind this schema and then use it to design a simple f factor algorithm for set cover, where f is the frequency of the most frequent element.
Unable to display preview. Download preview PDF.
- 63.G.B. Dantzig, L.R. Ford, and D.R. Fulkerson. A primal-dual algorithm for linear programs. In H.W. Kuhn and A.W. Tucker, editors, Linear Inequalities and Related Systems, pages 171–181. Princeton University Press, Princeton, NJ, 1956.Google Scholar
- 113.M.X. Goemans and D.P. Williamson. The primal—dual method for approximation algorithms and its applications to network design problems. In D.S. Hochbaum, editor, Approximation Algorithms for NP-Hard Problems, pages 144–191. PWS Publishing, Boston, MA, 1997.Google Scholar