Greedy approximations for minimum submodular cover with submodular cost

Authors:
Peng-Jun Wan;Ding-Zhu Du;Panos Pardalos;Weili Wu
Affiliations:
Department of Computer Science, Illinois Institute of Technology, Chicago, USA 60616;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75083;Department of Industrial Engineering and System Science, University of Florida, Gainsville, USA 32611;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75083
Venue:
Computational Optimization and Applications
Year:
2010

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Abstract

It is well-known that a greedy approximation with an integer-valued polymatroid potential function f is H(驴)-approximation of the minimum submodular cover problem with linear cost where 驴 is the maximum value of f over all singletons and H(驴) is the 驴-th harmonic number. In this paper, we establish similar results for the minimum submodular cover problem with a submodular cost (possibly nonlinear) and/or fractional submodular potential function f.