# American Institute of Mathematical Sciences

2015, 5(2): 91-100. doi: 10.3934/naco.2015.5.91

## Primal-dual approximation algorithms for submodular cost set cover problems with linear/submodular penalties

 1 Department of Information and Operations Research, College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, China, China 2 Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada 3 College of Science, Tianjin University of Technology, Tianjin 300384

Received  October 2014 Revised  April 2015 Published  June 2015

We introduce two set cover problems with submodular costs and linear/submodular penalties and offer two approximation algorithms of ratios $\eta$ and $2\eta$ respectively via the primal-dual technique, where $\eta$ is the largest number of sets that each element belongs to.
Citation: Fengmin Wang, Dachuan Xu, Donglei Du, Chenchen Wu. Primal-dual approximation algorithms for submodular cost set cover problems with linear/submodular penalties. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 91-100. doi: 10.3934/naco.2015.5.91
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