Greedy guarantees for minimum submodular cost submodular/non-submodular cover problem

Majun Shi, Zishen Yang and Wei Wang ()
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Majun Shi: Xi’an Jiaotong University
Zishen Yang: Xi’an Jiaotong University
Wei Wang: Xi’an Jiaotong University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 15, 16 pages

Abstract: Abstract Minimum Submodular Cost Submodular Cover problem (MIN-SCSC) often occurs naturally in the areas of combinatorial optimization and particularly machine learning. It is well-known that the greedy algorithm proposed by Wan et al. yields a $$\rho H(\delta )$$ ρ H ( δ ) -approximation for an integer-valued submodular function f, where $$\rho $$ ρ is the curvature of submodular cost function c, $$\delta $$ δ is the maximum value of f over all singletons and $$H(\delta )$$ H ( δ ) is the $$\delta $$ δ -th harmonic number (Wan et al. in Comput Optim Appl 45(2):463–474). In this paper, we first extend MIN-SCSC to Minimum Submodular Cost Non-submodular Cover problem and analyze the performances of the widely used greedy algorithm for integer-valued and fraction-valued potential functions respectively. In addition, we also study MIN-SCSC with fraction-valued potential functions, with a new analysis of the performance ratio of the greedy algorithm, improving upon the result of Wan et al. (2010).

Keywords: Greedy algorithm; Performance ratio; Submodular function; Submodular cover (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-022-00941-3

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