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

Fengmin  Wang; Dachuan  Xu; Donglei  Du; Chenchen Wu

doi:10.3934/naco.2015.5.91

Article Contents

2015, Volume 5, Issue 2: 91-100. Doi: 10.3934/naco.2015.5.91

This issue Previous Article Preface Next Article Complexity analysis of primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function with a trigonometric barrier term

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
2.
Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3
3.
College of Science, Tianjin University of Technology, Tianjin 300384

Received: October 2014

Revised: April 2015

Published: May 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C27; Secondary: 90C59.

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