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The maximum balanced subgraph of a signed graph: Applications and solution approaches

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  • Figueiredo, Rosa
  • Frota, Yuri

Abstract

The Maximum Balanced Subgraph Problem (MBSP) is the problem of finding a subgraph of a signed graph that is balanced and maximizes the cardinality of its vertex set. This paper is the first one to discuss applications of the MBSP arising in three different research areas: the detection of embedded structures, portfolio analysis in risk management and community structure. The efficient solution of the MBSP is also in the focus of this paper. We discuss pre-processing routines and heuristic solution approaches to the problem. a GRASP metaheuristic is developed and improved versions of a greedy heuristic are discussed. Extensive computational experiments are carried out on a set of instances from the applications previously mentioned as well as on a set of random instances.

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  • Figueiredo, Rosa & Frota, Yuri, 2014. "The maximum balanced subgraph of a signed graph: Applications and solution approaches," European Journal of Operational Research, Elsevier, vol. 236(2), pages 473-487.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:2:p:473-487
    DOI: 10.1016/j.ejor.2013.12.036
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    Cited by:

    1. Du, Haifeng & He, Xiaochen & Wang, Shanfeng & Gong, Maoguo & Feldman, Marcus W., 2017. "Optimizing transformations of structural balance in signed networks with potential relationships," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 414-424.
    2. Dewan F. Wahid & Elkafi Hassini, 2022. "A Literature Review on Correlation Clustering: Cross-disciplinary Taxonomy with Bibliometric Analysis," SN Operations Research Forum, Springer, vol. 3(3), pages 1-42, September.
    3. Mario Levorato & Rosa Figueiredo & Yuri Frota & Lúcia Drummond, 2017. "Evaluating balancing on social networks through the efficient solution of correlation clustering problems," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(4), pages 467-498, December.
    4. Eduardo Queiroga & Anand Subramanian & Rosa Figueiredo & Yuri Frota, 2021. "Integer programming formulations and efficient local search for relaxed correlation clustering," Journal of Global Optimization, Springer, vol. 81(4), pages 919-966, December.
    5. Zacharie Ales & Céline Engelbeen & Rosa Figueiredo, 2024. "Correlation Clustering Problem Under Mediation," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 672-689, March.

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