IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v349y2019icp359-366.html
   My bibliography  Save this article

A multi-start iterated greedy algorithm for the minimum weight vertex cover P3 problem

Author

Listed:
  • Zhang, Wenjie
  • Tu, Jianhua
  • Wu, Lidong

Abstract

Given a vertex-weighted graph G=(V,E) and a positive integer k ≥ 2, the minimum weight vertex cover Pk (MWVCPk) problem is to find a vertex subset F ⊆ V with minimum total weight such that every path of order k in G contains at least one vertex in F. For any integer k ≥ 2, the MWVCPk problem for general graphs is NP-hard. In this paper, we restrict our attention to the MWVCP3 problem and present a multi-start iterated greedy algorithm to solve the MWVCP3 problem. The experiments are carried out on randomly generated instances with up to 1000 vertices and 250000 edges. Our work is the first one to adopt heuristic algorithms to solve the MWVCP3 problem, and the experimental results show that our algorithm performs reasonably well in practice.

Suggested Citation

  • Zhang, Wenjie & Tu, Jianhua & Wu, Lidong, 2019. "A multi-start iterated greedy algorithm for the minimum weight vertex cover P3 problem," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 359-366.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:359-366
    DOI: 10.1016/j.amc.2018.12.067
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318311287
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.12.067?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. Hannes Moser & Rolf Niedermeier & Manuel Sorge, 2012. "Exact combinatorial algorithms and experiments for finding maximum k-plexes," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 347-373, October.
    2. Shyong Shyu & Peng-Yeng Yin & Bertrand Lin, 2004. "An Ant Colony Optimization Algorithm for the Minimum Weight Vertex Cover Problem," Annals of Operations Research, Springer, vol. 131(1), pages 283-304, October.
    3. Jianhua Tu & Lidong Wu & Jing Yuan & Lei Cui, 2017. "On the vertex cover $$P_3$$ P 3 problem parameterized by treewidth," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 414-425, August.
    4. Taoqing Zhou & Zhipeng Lü & Yang Wang & Junwen Ding & Bo Peng, 2016. "Multi-start iterated tabu search for the minimum weight vertex cover problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 368-384, August.
    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. Raka Jovanovic & Antonio P. Sanfilippo & Stefan Voß, 2022. "Fixed set search applied to the multi-objective minimum weighted vertex cover problem," Journal of Heuristics, Springer, vol. 28(4), pages 481-508, August.
    2. Luzhi Wang & Shuli Hu & Mingyang Li & Junping Zhou, 2019. "An Exact Algorithm for Minimum Vertex Cover Problem," Mathematics, MDPI, vol. 7(7), pages 1-8, July.
    3. Pedro Pinacho-Davidson & Christian Blum, 2020. "Barrakuda : A Hybrid Evolutionary Algorithm for Minimum Capacitated Dominating Set Problem," Mathematics, MDPI, vol. 8(11), pages 1-26, October.
    4. Luciano Ferreira Cruz & Flavia Bernardo Pinto & Lucas Camilotti & Angelo Marcio Oliveira Santanna & Roberto Zanetti Freire & Leandro Santos Coelho, 2022. "Improved multiobjective differential evolution with spherical pruning algorithm for optimizing 3D printing technology parametrization process," Annals of Operations Research, Springer, vol. 319(2), pages 1565-1587, December.
    5. Lin, B.M.T. & Lu, C.Y. & Shyu, S.J. & Tsai, C.Y., 2008. "Development of new features of ant colony optimization for flowshop scheduling," International Journal of Production Economics, Elsevier, vol. 112(2), pages 742-755, April.
    6. Jianhua Tu & Lidong Wu & Jing Yuan & Lei Cui, 2017. "On the vertex cover $$P_3$$ P 3 problem parameterized by treewidth," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 414-425, August.
    7. Shuli Hu & Xiaoli Wu & Huan Liu & Yiyuan Wang & Ruizhi Li & Minghao Yin, 2019. "Multi-Objective Neighborhood Search Algorithm Based on Decomposition for Multi-Objective Minimum Weighted Vertex Cover Problem," Sustainability, MDPI, vol. 11(13), pages 1-21, July.
    8. Lin Chen & Jin Peng & Bo Zhang & Shengguo Li, 2017. "Uncertain programming model for uncertain minimum weight vertex covering problem," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 625-632, March.
    9. Taoqing Zhou & Zhipeng Lü & Yang Wang & Junwen Ding & Bo Peng, 2016. "Multi-start iterated tabu search for the minimum weight vertex cover problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 368-384, August.
    10. Wayne Pullan, 2021. "Local search for the maximum k-plex problem," Journal of Heuristics, Springer, vol. 27(3), pages 303-324, June.
    11. Stefan Voßs & Andreas Fink & Cees Duin, 2005. "Looking Ahead with the Pilot Method," Annals of Operations Research, Springer, vol. 136(1), pages 285-302, April.

    More about this item

    Keywords

    Iterated greedy algorithm; Minimum weight vertex cover P3 problem; Heuristic algorithms; Combinatorial optimization problems;
    All these keywords.

    JEL classification:

    • P3 - Political Economy and Comparative Economic Systems - - Socialist Institutions and Their Transitions

    Statistics

    Access and download statistics

    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:349:y:2019:i:c:p:359-366. 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.