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Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning

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  • 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
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    References listed on IDEAS

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    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.
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