Abstract
In this paper, we introduce two variants of the submodular vertex cover problem, namely, the submodular vertex cover problems with linear and submodular penalties, for which we present two primal-dual approximation algorithms with approximation ratios of 2 and 4, respectively. Implementing the primal-dual framework directly on the dual programs of the linear program relaxations for these two variants cannot guarantee the dual ascending process terminates in polynomial time. To overcome this difficulty, we relax the two dual programs to slightly weaker versions which lead to two primal-dual approximation algorithms with the aforeclaimed approximation ratios.
An Erratum for this chapter can be found at http://dx.doi.org/10.1007/978-3-319-08783-2_61
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Xu, D., Wang, F., Du, D., Wu, C. (2014). Primal-Dual Approximation Algorithms for Submodular Vertex Cover Problems with Linear/Submodular Penalties. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_29
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DOI: https://doi.org/10.1007/978-3-319-08783-2_29
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