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An approximation algorithm for submodular hitting set problem with linear penalties

Author

Listed:
  • Shaojing Du

    (Hebei Normal University)

  • Suogang Gao

    (Hebei Normal University)

  • Bo Hou

    (Hebei Normal University)

  • Wen Liu

    (Hebei Normal University)

Abstract

The hitting set problem is a generalization of the vertex cover problem to hypergraphs. Xu et al. (Theor Comput Sci 630:117–125, 2016) presented a primal-dual algorithm for the submodular vertex cover problem with linear/submodular penalties. Motivated by their work, we study the submodular hitting set problem with linear penalties (SHSLP). The goal of the SHSLP is to select a vertex subset in the hypergraph to cover some hyperedges and penalize the uncovered ones such that the total cost of covering and penalty is minimized. Based on the primal-dual scheme, we obtain a k-approximation algorithm for the SHSLP, where k is the maximum number of vertices in all hyperedges.

Suggested Citation

  • Shaojing Du & Suogang Gao & Bo Hou & Wen Liu, 2020. "An approximation algorithm for submodular hitting set problem with linear penalties," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1065-1074, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00653-6
    DOI: 10.1007/s10878-020-00653-6
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    References listed on IDEAS

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    1. Yu Li & Donglei Du & Naihua Xiu & Dachuan Xu, 2014. "A unified dual-fitting approximation algorithm for the facility location problems with linear/submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 609-620, April.
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    Cited by:

    1. Xiaofei Liu & Weidong Li & Yaoyu Zhu, 2021. "Single Machine Vector Scheduling with General Penalties," Mathematics, MDPI, vol. 9(16), pages 1-16, August.

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