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Minimum non-submodular cover problem with applications

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  • Shi, Majun
  • Yang, Zishen
  • Wang, Wei

Abstract

Minimum Submodular Cover problem often occurs naturally in the context of combinatorial optimization. It is well-known that the greedy algorithm achieves an H(δ)-approximation guarantee for an integer-valued polymatroid potential function f, where δ is the maximum value of f over all singletons and H(δ) is the δ-th harmonic number. In this paper, we extend the setting into the non-submodular potential functions and investigate Minimum Non-submodular Cover problem with integer-valued and fraction-valued potential functions respectively, yielding similar performance results. In addition, we address several real-world applications which can be formulated as Minimum Non-submodular Cover problem.

Suggested Citation

  • Shi, Majun & Yang, Zishen & Wang, Wei, 2021. "Minimum non-submodular cover problem with applications," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005312
    DOI: 10.1016/j.amc.2021.126442
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    References listed on IDEAS

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    1. Ding-Zhu Du & Ker-I Ko & Xiaodong Hu, 2012. "Design and Analysis of Approximation Algorithms," Springer Optimization and Its Applications, Springer, number 978-1-4614-1701-9, June.
    2. Wolsey, L.A., 1982. "An analysis of the greedy algorithm for the submodular set covering problem," LIDAM Reprints CORE 519, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Majun Shi & Zishen Yang & Wei Wang, 2023. "Greedy guarantees for minimum submodular cost submodular/non-submodular cover problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-16, January.

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