IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v408y2021ics0096300321004471.html
   My bibliography  Save this article

Parallel approximation for partial set cover

Author

Listed:
  • Ran, Yingli
  • Zhang, Ying
  • Zhang, Zhao

Abstract

In a minimum partial set cover problem (MinPSC), given a ground set E with n elements, a collection S of subsets of E with |S|=m, a cost function c:S→R+, and an integer k≤n, the goal of MinPSC is to find a minimum cost sub-collection of S that covers at least k elements of E. In this paper, we design a parallel algorithm for MinPSC which yields a solution with approximation ratio at most f1−2ε in O(1εlogmnε) rounds, where f is the maximum number of sets containing a common element, and 0<ε<1/2 is a constant. We also design a parallel algorithm for a special MinPSC problem, the minimum power partial cover problem (MinPPC), which achieves approximation ratio at most (3+2ε)α1−2ε in O(1εlogmnεlog2m) rounds, where α≥1 is the attenuation factor of power.

Suggested Citation

  • Ran, Yingli & Zhang, Ying & Zhang, Zhao, 2021. "Parallel approximation for partial set cover," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    • Handle: RePEc:eee:apmaco:v:408:y:2021:i:c:s0096300321004471
    DOI: 10.1016/j.amc.2021.126358
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321004471
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126358?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Menghong Li & Yingli Ran & Zhao Zhang, 0. "A primal-dual algorithm for the minimum power partial cover problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-11.
    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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yingli Ran & Xiaohui Huang & Zhao Zhang & Ding-Zhu Du, 2021. "Approximation algorithm for minimum power partial multi-coverage in wireless sensor networks," Journal of Global Optimization, Springer, vol. 80(3), pages 661-677, July.
    2. Dongyue Liang & Zhao Zhang & Xianliang Liu & Wei Wang & Yaolin Jiang, 2016. "Approximation algorithms for minimum weight partial connected set cover problem," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 696-712, February.
    3. G. Calinescu & A. Zelikovsky, 2005. "The Polymatroid Steiner Problems," Journal of Combinatorial Optimization, Springer, vol. 9(3), pages 281-294, May.
    4. 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.
    5. Liao, Hao & Wu, Xingtong & Wang, Bing-Hong & Wu, Xiangyang & Zhou, Mingyang, 2019. "Solving the speed and accuracy of box-covering problem in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 954-963.
    6. Xu Zhu & Jieun Yu & Wonjun Lee & Donghyun Kim & Shan Shan & Ding-Zhu Du, 2010. "New dominating sets in social networks," Journal of Global Optimization, Springer, vol. 48(4), pages 633-642, December.
    7. Hao Zhong, 2024. "On greedy approximation algorithm for the minimum resolving dominating set problem," Journal of Combinatorial Optimization, Springer, vol. 48(4), pages 1-8, November.
    8. Weidong Chen & Hao Zhong & Lidong Wu & Ding-Zhu Du, 2022. "A general greedy approximation algorithm for finding minimum positive influence dominating sets in social networks," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 1-20, August.
    9. Shi, Majun & Yang, Zishen & Wang, Wei, 2021. "Minimum non-submodular cover problem with applications," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    10. Chandra Chekuri & Tanmay Inamdar & Kent Quanrud & Kasturi Varadarajan & Zhao Zhang, 2022. "Algorithms for covering multiple submodular constraints and applications," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 979-1010, September.
    11. Fatemeh Navidi & Prabhanjan Kambadur & Viswanath Nagarajan, 2020. "Adaptive Submodular Ranking and Routing," Operations Research, INFORMS, vol. 68(3), pages 856-877, May.
    12. Dana Angluin & James Aspnes & Lev Reyzin, 2015. "Network construction with subgraph connectivity constraints," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 418-432, February.
    13. Alfredo Torrico & Mohit Singh & Sebastian Pokutta & Nika Haghtalab & Joseph (Seffi) Naor & Nima Anari, 2021. "Structured Robust Submodular Maximization: Offline and Online Algorithms," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1590-1607, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:408:y:2021:i:c:s0096300321004471. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.