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An efficient local search algorithm for solving maximum edge weight clique problem in large graphs

Author

Listed:
  • Yi Chu

    (Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Boxiao Liu

    (Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Shaowei Cai

    (Chinese Academy of Sciences)

  • Chuan Luo

    (Leiden University
    Microsoft Research)

  • Haihang You

    (Chinese Academy of Sciences)

Abstract

Maximum vertex weight clique problem (MVWCP) and maximum edge weight clique problem (MEWCP) are two significant generalizations of maximum clique problem (MCP), and can be widely used in many real-world applications including molecular biology, broadband network design and pattern recognition. Recently, breakthroughs have been made for solving MVWCP in large graphs, resulting in several state-of-the-art algorithms, such as WLMC, FastWClq and LSCC + BMS. However, less attention has been paid to solving MEWCP in large graphs. In this paper, we present an efficient Stochastic Local Search (SLS) algorithm for MEWCP by combining clique construction, local search and graph reduction, resulting in a new algorithm named ReConSLS. We also propose a new upper bound function for edge weighted graphs which is essential for graph reduction. Extensive experiments on a wide range of large graphs demonstrate that ReConSLS surpasses state-of-the-art SLS competitors on the majority of testing graphs.

Suggested Citation

  • Yi Chu & Boxiao Liu & Shaowei Cai & Chuan Luo & Haihang You, 2020. "An efficient local search algorithm for solving maximum edge weight clique problem in large graphs," Journal of Combinatorial Optimization, Springer, vol. 39(4), pages 933-954, May.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:4:d:10.1007_s10878-020-00529-9
    DOI: 10.1007/s10878-020-00529-9
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    References listed on IDEAS

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    1. Wayne Pullan, 2006. "Phased local search for the maximum clique problem," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 303-323, November.
    2. Qinghua Wu & Jin-Kao Hao & Fred Glover, 2012. "Multi-neighborhood tabu search for the maximum weight clique problem," Annals of Operations Research, Springer, vol. 196(1), pages 611-634, July.
    3. Haochen Zhang & Shaowei Cai & Chuan Luo & Minghao Yin, 2017. "An efficient local search algorithm for the winner determination problem," Journal of Heuristics, Springer, vol. 23(5), pages 367-396, October.
    4. Alidaee, Bahram & Glover, Fred & Kochenberger, Gary & Wang, Haibo, 2007. "Solving the maximum edge weight clique problem via unconstrained quadratic programming," European Journal of Operational Research, Elsevier, vol. 181(2), pages 592-597, September.
    5. Park, Kyungchul & Lee, Kyungsik & Park, Sungsoo, 1996. "An extended formulation approach to the edge-weighted maximal clique problem," European Journal of Operational Research, Elsevier, vol. 95(3), pages 671-682, December.
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    2. Jun Wu & Minghao Yin, 2021. "A Restart Local Search for Solving Diversified Top- k Weight Clique Search Problem," Mathematics, MDPI, vol. 9(21), pages 1-17, October.

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