IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2021i1p97-d712805.html
   My bibliography  Save this article

Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning

Author

Listed:
  • Kristjan Reba

    (Theory Department, National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia
    Faculty of Computer and Information Science, University of Ljubljana, Večna Pot 113, 1000 Ljubljana, Slovenia)

  • Matej Guid

    (Faculty of Computer and Information Science, University of Ljubljana, Večna Pot 113, 1000 Ljubljana, Slovenia)

  • Kati Rozman

    (Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Glagoljaška ulica 8, 6000 Koper, Slovenia)

  • Dušanka Janežič

    (Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Glagoljaška ulica 8, 6000 Koper, Slovenia)

  • Janez Konc

    (Theory Department, National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia)

Abstract

Finding a maximum clique is important in research areas such as computational chemistry, social network analysis, and bioinformatics. It is possible to compare the maximum clique size between protein graphs to determine their similarity and function. In this paper, improvements based on machine learning (ML) are added to a dynamic algorithm for finding the maximum clique in a protein graph, Maximum Clique Dynamic (MaxCliqueDyn; short: MCQD). This algorithm was published in 2007 and has been widely used in bioinformatics since then. It uses an empirically determined parameter, Tlimit, that determines the algorithm’s flow. We have extended the MCQD algorithm with an initial phase of a machine learning-based prediction of the Tlimit parameter that is best suited for each input graph. Such adaptability to graph types based on state-of-the-art machine learning is a novel approach that has not been used in most graph-theoretic algorithms. We show empirically that the resulting new algorithm MCQD-ML improves search speed on certain types of graphs, in particular molecular docking graphs used in drug design where they determine energetically favorable conformations of small molecules in a protein binding site. In such cases, the speed-up is twofold.

Suggested Citation

  • Kristjan Reba & Matej Guid & Kati Rozman & Dušanka Janežič & Janez Konc, 2021. "Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning," Mathematics, MDPI, vol. 10(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:97-:d:712805
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/1/97/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/1/97/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wu, Qinghua & Hao, Jin-Kao, 2015. "A review on algorithms for maximum clique problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 693-709.
    2. Butenko, S. & Wilhelm, W.E., 2006. "Clique-detection models in computational biochemistry and genomics," European Journal of Operational Research, Elsevier, vol. 173(1), pages 1-17, 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. Foad Mahdavi Pajouh, 2020. "Minimum cost edge blocker clique problem," Annals of Operations Research, Springer, vol. 294(1), pages 345-376, November.
    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. Oleksandra Yezerska & Sergiy Butenko & Vladimir L. Boginski, 2018. "Detecting robust cliques in graphs subject to uncertain edge failures," Annals of Operations Research, Springer, vol. 262(1), pages 109-132, March.
    4. Li, Chu-Min & Liu, Yanli & Jiang, Hua & Manyà, Felip & Li, Yu, 2018. "A new upper bound for the maximum weight clique problem," European Journal of Operational Research, Elsevier, vol. 270(1), pages 66-77.
    5. Stefano Coniglio & Stefano Gualandi, 2022. "Optimizing over the Closure of Rank Inequalities with a Small Right-Hand Side for the Maximum Stable Set Problem via Bilevel Programming," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1006-1023, March.
    6. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2020. "A Lagrangian Bound on the Clique Number and an Exact Algorithm for the Maximum Edge Weight Clique Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 747-762, July.
    7. Laurent, Monique & Vargas, Luis Felipe, 2022. "Finite convergence of sum-of-squares hierarchies for the stability number of a graph," Other publications TiSEM 3998b864-7504-4cf4-bc1d-f, Tilburg University, School of Economics and Management.
    8. Lehouillier, Thibault & Omer, Jérémy & Soumis, François & Desaulniers, Guy, 2017. "Two decomposition algorithms for solving a minimum weight maximum clique model for the air conflict resolution problem," European Journal of Operational Research, Elsevier, vol. 256(3), pages 696-712.
    9. 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.
    10. 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.
    11. 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.
    12. Rosanna Grassi & Paolo Bartesaghi & Stefano Benati & Gian Paolo Clemente, 2021. "Multi-Attribute Community Detection in International Trade Network," Networks and Spatial Economics, Springer, vol. 21(3), pages 707-733, September.
    13. 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.
    14. Zhou, Yi & Hao, Jin-Kao & Goëffon, Adrien, 2017. "PUSH: A generalized operator for the Maximum Vertex Weight Clique Problem," European Journal of Operational Research, Elsevier, vol. 257(1), pages 41-54.
    15. San Segundo, Pablo & Coniglio, Stefano & Furini, Fabio & Ljubić, Ivana, 2019. "A new branch-and-bound algorithm for the maximum edge-weighted clique problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 76-90.
    16. Nasirian, Farzaneh & Mahdavi Pajouh, Foad & Balasundaram, Balabhaskar, 2020. "Detecting a most closeness-central clique in complex networks," European Journal of Operational Research, Elsevier, vol. 283(2), pages 461-475.
    17. Filipa D. Carvalho & Maria Teresa Almeida, 2017. "The triangle k-club problem," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 814-846, April.
    18. 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.
    19. Evgeny Maslov & Mikhail Batsyn & Panos Pardalos, 2014. "Speeding up branch and bound algorithms for solving the maximum clique problem," Journal of Global Optimization, Springer, vol. 59(1), pages 1-21, May.
    20. Alessio Troiani, 2024. "Probabilistic Cellular Automata Monte Carlo for the Maximum Clique Problem," Mathematics, MDPI, vol. 12(18), pages 1-16, September.

    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:gam:jmathe:v:10:y:2021:i:1:p:97-:d:712805. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.