Abstract
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.
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H.W. Kuhn. The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2: 83–97, 1955.
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.
R. Bar-Yehuda and S. Even. A linear-time approximation algorithm for the weighted vertex cover problem. Journal of Algorithms, 2: 198–203, 1981.
A. Agrawal, P. Klein, and R. Ravi. When trees collide: an approximation algorithm for the generalized Steiner network problem on networks. SIAM Journal on Computing, 24: 440–456, 1995.
M.X. Goemans and D.P. Williamson. A general approximation technique for constrained forest problems. SIAM Journal on Computing, 24: 296–317, 1995.
D.P. Williamson, M.X. Goemans, M. Mihail, and V.V. Vazirani. A primal-dual approximation algorithm for generalized Steiner network problems. Combinatorica, 15: 435–454, 1995.
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.
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Vazirani, V.V. (2003). Set Cover via the Primal-Dual Schema. In: Approximation Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04565-7_15
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DOI: https://doi.org/10.1007/978-3-662-04565-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08469-0
Online ISBN: 978-3-662-04565-7
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