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Maximum Weight Relaxed Cliques and Russian Doll Search Revisited

Author

Listed:
  • Timo Gschwind

    (Johannes Gutenberg-Universität Mainz, Germany)

  • Stefan Irnich

    (Johannes Gutenberg-Universität Mainz, Germany)

  • Isabel Podlinski

    (Zalando SE, Germany)

Abstract

Trukhanov et al. [Trukhanov S, Balasubramaniam C, Balasundaram B, Butenko S (2013) Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations. Comp. Opt. and Appl., 56(1), 113–130] used the Russian Doll Search (RDS) principle to effectively find maximum hereditary structures in graphs. Prominent examples of such hereditary structures are cliques and some clique relaxations intensely discussed and studied in network analysis. The effectiveness of the tailored RDS by Trukhanov et al. for s-plex and s-defective clique can be attributed to their cleverly designed incremental verification procedures used to distinguish feasible from infeasible structures. In this short note, we clarify the incompletely presented verification procedure for s-plex and present a new and simpler incremental verification procedure for s-defective cliques with a better worst-case runtime. Furthermore, we develop an incremental verification for s-bundle, giving rise to the first exact algorithm for solving the maximum cardinality and maximum weight s-bundle problems.

Suggested Citation

  • Timo Gschwind & Stefan Irnich & Isabel Podlinski, 2015. "Maximum Weight Relaxed Cliques and Russian Doll Search Revisited," Working Papers 1504, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 19 May 2015.
    • Handle: RePEc:jgu:wpaper:1504
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    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1504.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Pattillo, Jeffrey & Youssef, Nataly & Butenko, Sergiy, 2013. "On clique relaxation models in network analysis," European Journal of Operational Research, Elsevier, vol. 226(1), pages 9-18.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Timo Gschwind & Stefan Irnich & Fabio Furini & Roberto Wol?er Calvo, 2015. "Social Network Analysis and Community Detection by Decomposing a Graph into Relaxed Cliques," Working Papers 1520, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

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    More about this item

    Keywords

    Relaxed clique; Russian Doll Search; Optimal hereditary structures; Maximum weight problem;
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