Abstract
We will introduce the technique of LP-rounding by using it to design two approximation algorithms for the set cover problem, Problem 2.1. The first is a simple rounding algorithm achieving a guarantee of f, where f is the frequency of the most frequent element. The second algorithm, achieving an approximation guarantee of O(log n), illustrates the use of randomization in rounding.
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Notes
D.S. Hochbaum. Approximation algorithms for the set covering and vertex cover problems. SIAM Journal on Computing, 11:555–556, 1982. (Cited on pp. 25, 123 )
A. Srinivasan. Improved approximations of packing and covering problems. In Proc. 27th ACM Symposium on the Theory of Computing,pages 268–276, 1995. (Cited on p. 123)
G.L. Nemhauser and L.E. Trotter. Vertex packings: structural properties and algorithms. Mathematical Programming,8:232–248, 1975. (Cited on p. 123)
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© 2003 Springer-Verlag Berlin Heidelberg
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Vazirani, V.V. (2003). Rounding Applied to Set Cover. In: Approximation Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04565-7_14
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DOI: https://doi.org/10.1007/978-3-662-04565-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08469-0
Online ISBN: 978-3-662-04565-7
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