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Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations

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  • Svyatoslav Trukhanov
  • Chitra Balasubramaniam
  • Balabhaskar Balasundaram
  • Sergiy Butenko

Abstract

Given a simple undirected graph, the problem of finding a maximum subset of vertices satisfying a nontrivial, interesting property Π that is hereditary on induced subgraphs, is known to be NP-hard. Many well-known graph properties meet the above conditions, making the problem widely applicable. This paper proposes a general purpose exact algorithmic framework to solve this problem and investigates key algorithm design and implementation issues that are helpful in tailoring the general framework for specific graph properties. The performance of the algorithms so derived for the maximum s-plex and the maximum s-defective clique problems, which arise in network-based data mining applications, is assessed through a computational study. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:56:y:2013:i:1:p:113-130
    DOI: 10.1007/s10589-013-9548-5
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    References listed on IDEAS

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    3. Benjamin McClosky & Illya V. Hicks, 2012. "Combinatorial algorithms for the maximum k-plex problem," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 29-49, January.
    4. E. C. Sewell, 1998. "A Branch and Bound Algorithm for the Stability Number of a Sparse Graph," INFORMS Journal on Computing, INFORMS, vol. 10(4), pages 438-447, November.
    5. 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.
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    Cited by:

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    2. Alexander Veremyev & Oleg A. Prokopyev & Sergiy Butenko & Eduardo L. Pasiliao, 2016. "Exact MIP-based approaches for finding maximum quasi-cliques and dense subgraphs," Computational Optimization and Applications, Springer, vol. 64(1), pages 177-214, May.
    3. Timo Gschwind & Stefan Irnich & Fabio Furini & Roberto Wolfler Calvo, 2021. "A Branch-and-Price Framework for Decomposing Graphs into Relaxed Cliques," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1070-1090, July.
    4. Timo Gschwind & Stefan Irnich & Fabio Furini & Roberto Wolfler Calvo, 2017. "A Branch-and-Price Framework for Decomposing Graphs into Relaxed Cliques," Working Papers 1723, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    5. Timo Gschwind & Stefan Irnich & Fabio Furini & Roberto Wolfler Calvo, 2017. "Social Network Analysis and Community Detection by Decomposing a Graph into Relaxed Cliques," Working Papers 1722, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    6. Zhuqi Miao & Balabhaskar Balasundaram & Eduardo L. Pasiliao, 2014. "An exact algorithm for the maximum probabilistic clique problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 105-120, July.
    7. Bruno Nogueira & Rian G. S. Pinheiro, 2020. "A GPU based local search algorithm for the unweighted and weighted maximum s-plex problems," Annals of Operations Research, Springer, vol. 284(1), pages 367-400, January.
    8. Zeynep Ertem & Eugene Lykhovyd & Yiming Wang & Sergiy Butenko, 2020. "The maximum independent union of cliques problem: complexity and exact approaches," Journal of Global Optimization, Springer, vol. 76(3), pages 545-562, March.
    9. Maciej Rysz & Foad Mahdavi Pajouh & Pavlo Krokhmal & Eduardo L. Pasiliao, 2018. "Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights," Annals of Operations Research, Springer, vol. 262(1), pages 89-108, March.
    10. Şuvak, Zeynep & Altınel, İ. Kuban & Aras, Necati, 2020. "Exact solution algorithms for the maximum flow problem with additional conflict constraints," European Journal of Operational Research, Elsevier, vol. 287(2), pages 410-437.
    11. Tuan Le & Jon M. Stauffer & Bala Shetty & Chelliah Sriskandarajah, 2023. "An optimization framework for analyzing dual‐donor organ exchange," Production and Operations Management, Production and Operations Management Society, vol. 32(3), pages 740-761, March.
    12. 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.
    13. Maciej Rysz & Mohammad Mirghorbani & Pavlo Krokhmal & Eduardo L. Pasiliao, 2014. "On risk-averse maximum weighted subgraph problems," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 167-185, July.
    14. Zhuqi Miao & Balabhaskar Balasundaram, 2020. "An Ellipsoidal Bounding Scheme for the Quasi-Clique Number of a Graph," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 763-778, July.
    15. 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.
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