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Greedy approximations for minimum submodular cover with submodular cost

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Abstract

It is well-known that a greedy approximation with an integer-valued polymatroid potential function f is H(γ)-approximation of the minimum submodular cover problem with linear cost where γ is the maximum value of f over all singletons and H(γ) is the γ-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.

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References

  1. Baudis, G., Gröpl, C., Hougardy, S., Nierhoff, T., Prömel, H.J.: Approximating minimum spanning sets in hypergraphs and polymatroids. Technical Report, Humboldt-Universitt zu Berlin (2000)

  2. Calinescu, G., Kapoor, S., Olshevsky, A., Zelikovsky, A.: Network lifetime and power assignment in ad hoc wireless networks. In: Lectures Notes in Computer Science, vol. 2832, pp. 114–126. Springer, Berlin (2003)

    Google Scholar 

  3. Feige, U.: A threshold of ln n for approximating set cover. In: Proc. the Twenty-Eighth Annual ACM Symp. Theory of Computing, pp. 314–318 (1996)

  4. Fujito, T.: Approximation algorithms for submodular set cover with application. IEICE Trans. Inf. Syst. E83-D(3), 480–487 (2000)

    Google Scholar 

  5. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, New York (1999)

    MATH  Google Scholar 

  6. Wolsey, L.A.: An analysis of the greedy algorithm for submodular set covering problem. Combinatorica 2(4), 385–393 (1982)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Illinois Institute of Technology, Chicago, IL, 60616, USA

    Peng-Jun Wan

  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75083, USA

    Ding-Zhu Du & Weili Wu

  3. Department of Industrial Engineering and System Science, University of Florida, Gainsville, FL, 32611, USA

    Panos Pardalos

Authors
  1. Peng-Jun Wan
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  2. Ding-Zhu Du
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  3. Panos Pardalos
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  4. Weili Wu
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Corresponding author

Correspondence to Panos Pardalos.

Additional information

The work of P.-J. Wan was partially supported by National Science Foundation of USA under grant CNS-0831831.

The work of D.-Z. Du was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 1165/04E] and also partially supported by National Science Foundation of USA under grant CCF-0728851.

The work of W. Wu was supported in part by National Science Foundation of USA under grant CCF-9208913.

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Wan, PJ., Du, DZ., Pardalos, P. et al. Greedy approximations for minimum submodular cover with submodular cost. Comput Optim Appl 45, 463–474 (2010). https://doi.org/10.1007/s10589-009-9269-y

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  • DOI: https://doi.org/10.1007/s10589-009-9269-y

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