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Using Modular Decomposition Technique to Solve the Maximum Clique Problem

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Computational Aspects and Applications in Large-Scale Networks (NET 2016)

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Abstract

In this article, we use the modular decomposition technique to solve the weighted maximum clique problem exactly. Proposed algorithm takes the modular decomposition tree, constructed in linear time, and finds maximum weighted clique via recursive tree search (DFS). We want to show that modular decomposition reduces calculation time. However, not all graphs have modules, so in the article there are algorithms to construct them. The results show comparison of proposed solution with Ostergard’s algorithm on DIMACS benchmarks and on generated graphs.

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Acknowledgements

The author is grateful to Dmitry Malyshev for the problem statement and fruitful discussions.

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Authors and Affiliations

  1. Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics, 136, Rodionova Str., Nizhny Novgorod, Russia

    Irina Utkina

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  1. Irina Utkina
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Correspondence to Irina Utkina .

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Editors and Affiliations

  1. Higher School of Economics, National Research University, Nizhny Novgorod, Russia

    Valery A. Kalyagin

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  3. Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA

    Oleg Prokopyev

  4. Higher School of Economics, National Research University, Nizhny Novgorod, Russia

    Irina Utkina

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Utkina, I. (2018). Using Modular Decomposition Technique to Solve the Maximum Clique Problem. In: Kalyagin, V., Pardalos, P., Prokopyev, O., Utkina, I. (eds) Computational Aspects and Applications in Large-Scale Networks. NET 2016. Springer Proceedings in Mathematics & Statistics, vol 247. Springer, Cham. https://doi.org/10.1007/978-3-319-96247-4_8

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