IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v24y2012i3d10.1007_s10878-011-9391-5.html
   My bibliography  Save this article

Exact combinatorial algorithms and experiments for finding maximum k-plexes

Author

Listed:
  • Hannes Moser

    (TU Berlin)

  • Rolf Niedermeier

    (TU Berlin)

  • Manuel Sorge

    (TU Berlin)

Abstract

We propose new practical algorithms to find maximum-cardinality k-plexes in graphs. A k-plex denotes a vertex subset in a graph inducing a subgraph where every vertex has edges to all but at most k vertices in the k-plex. Cliques are 1-plexes. In analogy to the special case of finding maximum-cardinality cliques, finding maximum-cardinality k-plexes is NP-hard. Complementing previous work, we develop exact combinatorial algorithms, which are strongly based on methods from parameterized algorithmics. The experiments with our freely available implementation indicate the competitiveness of our approach, for many real-world graphs outperforming the previously used methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9391-5
    DOI: 10.1007/s10878-011-9391-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-011-9391-5
    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/s10878-011-9391-5?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. Laura A. Sanchis & Arun Jagota, 1996. "Some Experimental and Theoretical Results on Test Case Generators for the Maximum Clique Problem," INFORMS Journal on Computing, INFORMS, vol. 8(2), pages 87-102, May.
    2. Balabhaskar Balasundaram & Sergiy Butenko & Svyatoslav Trukhanov, 2005. "Novel Approaches for Analyzing Biological Networks," Journal of Combinatorial Optimization, Springer, vol. 10(1), pages 23-39, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Wayne Pullan, 2021. "Local search for the maximum k-plex problem," Journal of Heuristics, Springer, vol. 27(3), pages 303-324, June.
    3. 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.

    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. 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.
    2. Carvalho, Filipa D. & Almeida, M. Teresa, 2011. "Upper bounds and heuristics for the 2-club problem," European Journal of Operational Research, Elsevier, vol. 210(3), pages 489-494, May.
    3. Grigory Pastukhov & Alexander Veremyev & Vladimir Boginski & Eduardo L. Pasiliao, 2014. "Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 462-486, April.
    4. Veremyev, Alexander & Boginski, Vladimir & Pasiliao, Eduardo L. & Prokopyev, Oleg A., 2022. "On integer programming models for the maximum 2-club problem and its robust generalizations in sparse graphs," European Journal of Operational Research, Elsevier, vol. 297(1), pages 86-101.
    5. Oleksandra Yezerska & Foad Mahdavi Pajouh & Alexander Veremyev & Sergiy Butenko, 2019. "Exact algorithms for the minimum s-club partitioning problem," Annals of Operations Research, Springer, vol. 276(1), pages 267-291, May.
    6. Veremyev, Alexander & Boginski, Vladimir, 2012. "Identifying large robust network clusters via new compact formulations of maximum k-club problems," European Journal of Operational Research, Elsevier, vol. 218(2), pages 316-326.
    7. Komusiewicz, Christian & Nichterlein, André & Niedermeier, Rolf & Picker, Marten, 2019. "Exact algorithms for finding well-connected 2-clubs in sparse real-world graphs: Theory and experiments," European Journal of Operational Research, Elsevier, vol. 275(3), pages 846-864.
    8. Niels Grüttemeier & Philipp Heinrich Keßler & Christian Komusiewicz & Frank Sommer, 2024. "Efficient branch-and-bound algorithms for finding triangle-constrained 2-clubs," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-27, October.
    9. Filipa D. Carvalho & Maria Teresa Almeida, 2017. "The triangle k-club problem," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 814-846, April.
    10. Alexander Veremyev & Vladimir Boginski & Eduardo Pasiliao, 2015. "Analytical characterizations of some classes of optimal strongly attack-tolerant networks and their Laplacian spectra," Journal of Global Optimization, Springer, vol. 61(1), pages 109-138, January.
    11. Foad Mahdavi Pajouh & Balabhaskar Balasundaram & Illya V. Hicks, 2016. "On the 2-Club Polytope of Graphs," Operations Research, INFORMS, vol. 64(6), pages 1466-1481, December.
    12. Yezerska, Oleksandra & Mahdavi Pajouh, Foad & Butenko, Sergiy, 2017. "On biconnected and fragile subgraphs of low diameter," European Journal of Operational Research, Elsevier, vol. 263(2), pages 390-400.
    13. Chitra Balasubramaniam & Sergiy Butenko, 2017. "On robust clusters of minimum cardinality in networks," Annals of Operations Research, Springer, vol. 249(1), pages 17-37, February.
    14. 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.
    15. Maciej Rysz & Foad Mahdavi Pajouh & Pavlo Krokhmal & Eduardo L. Pasiliao, 2018. "Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights," Annals of Operations Research, Springer, vol. 262(1), pages 89-108, March.
    16. Alexander Veremyev & Oleg A. Prokopyev & Sergiy Butenko & Eduardo L. Pasiliao, 2016. "Exact MIP-based approaches for finding maximum quasi-cliques and dense subgraphs," Computational Optimization and Applications, Springer, vol. 64(1), pages 177-214, May.
    17. Buchanan, Austin & Sung, Je Sang & Boginski, Vladimir & Butenko, Sergiy, 2014. "On connected dominating sets of restricted diameter," European Journal of Operational Research, Elsevier, vol. 236(2), pages 410-418.
    18. Balasundaram, Balabhaskar & Borrero, Juan S. & Pan, Hao, 2022. "Graph signatures: Identification and optimization," European Journal of Operational Research, Elsevier, vol. 296(3), pages 764-775.
    19. 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.
    20. Andrew C. Trapp & Oleg A. Prokopyev, 2010. "Solving the Order-Preserving Submatrix Problem via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 387-400, August.

    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:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9391-5. 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.