IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v27y2021i3d10.1007_s10732-020-09459-5.html
   My bibliography  Save this article

Local search for the maximum k-plex problem

Author

Listed:
  • Wayne Pullan

    (Griffith University)

Abstract

The maximum k-plex problem is an important, computationally complex graph based problem. In this study an effective k-plex local search (KLS) is presented for solving this problem on a wide range of graph types. KLS uses data structures suitable for the graph being analysed and has mechanisms for preventing search cycling and promoting search diversity. State of the art results were obtained on 121 dense graphs and 61 large real-life (sparse) graphs. Comparisons with three recent algorithms on the more difficult graphs show that KLS performed better or as well as in 93% of 332 significant k-plex problem instances investigated achieving either larger average k-plex sizes (including some new results) or, when these were equivalent, lower CPU requirements.

Suggested Citation

  • Wayne Pullan, 2021. "Local search for the maximum k-plex problem," Journal of Heuristics, Springer, vol. 27(3), pages 303-324, June.
    • Handle: RePEc:spr:joheur:v:27:y:2021:i:3:d:10.1007_s10732-020-09459-5
    DOI: 10.1007/s10732-020-09459-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-020-09459-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10732-020-09459-5?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. Balabhaskar Balasundaram & Sergiy Butenko & Illya V. Hicks, 2011. "Clique Relaxations in Social Network Analysis: The Maximum k -Plex Problem," Operations Research, INFORMS, vol. 59(1), pages 133-142, February.
    2. Svyatoslav Trukhanov & Chitra Balasubramaniam & Balabhaskar Balasundaram & Sergiy Butenko, 2013. "Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations," Computational Optimization and Applications, Springer, vol. 56(1), pages 113-130, September.
    3. 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.
    4. Benjamin McClosky & Illya V. Hicks, 2012. "Combinatorial algorithms for the maximum k-plex problem," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 29-49, January.
    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. Bruno Nogueira & Rian G. S. Pinheiro, 2020. "A GPU based local search algorithm for the unweighted and weighted maximum s-plex problems," Annals of Operations Research, Springer, vol. 284(1), pages 367-400, January.
    2. Zhou, Yi & Lin, Weibo & Hao, Jin-Kao & Xiao, Mingyu & Jin, Yan, 2022. "An effective branch-and-bound algorithm for the maximum s-bundle problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 27-39.
    3. Timo Gschwind & Stefan Irnich & Fabio Furini & Roberto Wolfler Calvo, 2017. "A Branch-and-Price Framework for Decomposing Graphs into Relaxed Cliques," Working Papers 1723, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. Zhuqi Miao & Balabhaskar Balasundaram, 2020. "An Ellipsoidal Bounding Scheme for the Quasi-Clique Number of a Graph," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 763-778, July.
    5. Timo Gschwind & Stefan Irnich & Fabio Furini & Roberto Wolfler Calvo, 2017. "Social Network Analysis and Community Detection by Decomposing a Graph into Relaxed Cliques," Working Papers 1722, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    6. Timo Gschwind & Stefan Irnich & Fabio Furini & Roberto Wolfler Calvo, 2021. "A Branch-and-Price Framework for Decomposing Graphs into Relaxed Cliques," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1070-1090, July.
    7. David Bergman & Andre A. Cire & Willem-Jan van Hoeve & J. N. Hooker, 2016. "Discrete Optimization with Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 47-66, February.
    8. Svyatoslav Trukhanov & Chitra Balasubramaniam & Balabhaskar Balasundaram & Sergiy Butenko, 2013. "Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations," Computational Optimization and Applications, Springer, vol. 56(1), pages 113-130, September.
    9. Zhuqi Miao & Balabhaskar Balasundaram & Eduardo L. Pasiliao, 2014. "An exact algorithm for the maximum probabilistic clique problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 105-120, July.
    10. Benjamin McClosky & John D. Arellano & Illya V. Hicks, 2015. "Co-2-plex vertex partitions," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 729-746, October.
    11. S. Raghavan & Rui Zhang, 2022. "Rapid Influence Maximization on Social Networks: The Positive Influence Dominating Set Problem," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1345-1365, May.
    12. 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.
    13. Filipa D. Carvalho & Maria Teresa Almeida, 2017. "The triangle k-club problem," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 814-846, April.
    14. Maciej Rysz & Mohammad Mirghorbani & Pavlo Krokhmal & Eduardo L. Pasiliao, 2014. "On risk-averse maximum weighted subgraph problems," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 167-185, July.
    15. Zhou, Yi & Rossi, André & Hao, Jin-Kao, 2018. "Towards effective exact methods for the Maximum Balanced Biclique Problem in bipartite graphs," European Journal of Operational Research, Elsevier, vol. 269(3), pages 834-843.
    16. Assif Assad & Kusum Deep, 2018. "A heuristic based harmony search algorithm for maximum clique problem," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 411-433, June.
    17. Yuan Sun & Andreas Ernst & Xiaodong Li & Jake Weiner, 2021. "Generalization of machine learning for problem reduction: a case study on travelling salesman problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 607-633, September.
    18. Timo Gschwind & Stefan Irnich & Isabel Podlinski, 2015. "Maximum Weight Relaxed Cliques and Russian Doll Search Revisited," Working Papers 1504, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 19 May 2015.
    19. S. Raghavan & Rui Zhang, 2022. "Influence Maximization with Latency Requirements on Social Networks," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 710-728, March.
    20. Şuvak, Zeynep & Altınel, İ. Kuban & Aras, Necati, 2020. "Exact solution algorithms for the maximum flow problem with additional conflict constraints," European Journal of Operational Research, Elsevier, vol. 287(2), pages 410-437.

    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:spr:joheur:v:27:y:2021:i:3:d:10.1007_s10732-020-09459-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.