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Speeding up branch and bound algorithms for solving the maximum clique problem

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  • Evgeny Maslov
  • Mikhail Batsyn
  • Panos Pardalos

Abstract

In this paper we consider two branch and bound algorithms for the maximum clique problem which demonstrate the best performance on DIMACS instances among the existing methods. These algorithms are MCS algorithm by Tomita et al. ( 2010 ) and MAXSAT algorithm by Li and Quan ( 2010a , b ). We suggest a general approach which allows us to speed up considerably these branch and bound algorithms on hard instances. The idea is to apply a powerful heuristic for obtaining an initial solution of high quality. This solution is then used to prune branches in the main branch and bound algorithm. For this purpose we apply ILS heuristic by Andrade et al. (J Heuristics 18(4):525–547, 2012 ). The best results are obtained for p_hat1000-3 instance and gen instances with up to 11,000 times speedup. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:1:p:1-21
    DOI: 10.1007/s10898-013-0075-9
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    1. Jenelius, Erik & Petersen, Tom & Mattsson, Lars-Göran, 2006. "Importance and exposure in road network vulnerability analysis," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(7), pages 537-560, August.
    2. Anna Nagurney (ed.), 2003. "Innovations in Financial and Economic Networks," Books, Edward Elgar Publishing, number 3116.
    3. 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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    Cited by:

    1. Yuichi Asahiro & Tomohiro Kubo & Eiji Miyano, 2019. "Experimental Evaluation of Approximation and Heuristic Algorithms for Maximum Distance-Bounded Subgraph Problems," The Review of Socionetwork Strategies, Springer, vol. 13(2), pages 143-161, October.
    2. 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.
    3. Coniglio, Stefano & Furini, Fabio & San Segundo, Pablo, 2021. "A new combinatorial branch-and-bound algorithm for the Knapsack Problem with Conflicts," European Journal of Operational Research, Elsevier, vol. 289(2), pages 435-455.
    4. San Segundo, Pablo & Furini, Fabio & Álvarez, David & Pardalos, Panos M., 2023. "CliSAT: A new exact algorithm for hard maximum clique problems," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1008-1025.
    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. 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.

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