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Integer programming formulations and efficient local search for relaxed correlation clustering

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Abstract

Relaxed correlation clustering (RCC) is a vertex partitioning problem that aims at minimizing the so-called relaxed imbalance in signed graphs. RCC is considered to be an NP-hard unsupervised learning problem with applications in biology, economy, image recognition and social network analysis. In order to solve it, we propose two linear integer programming formulations and a local search-based metaheuristic. The latter relies on auxiliary data structures to efficiently perform move evaluations during the search process. Extensive computational experiments on existing and newly proposed benchmark instances demonstrate the superior performance of the proposed approaches when compared to those available in the literature. While the exact approaches obtained optimal solutions for open problems, the proposed heuristic algorithm was capable of finding high quality solutions within a reasonable CPU time. In addition, we also report improving results for the symmetrical version of the problem. Moreover, we show the benefits of implementing the efficient move evaluation procedure that enables the proposed metaheuristic to be scalable, even for large-size instances.

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Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior–Brasil (CAPES)–Finance Code 001 and by the Conselho Nacional de Desenvolvimento Cientfífico e Tecnológico (CNPq), grants 305223/2015-1 and 303799/2018-8. We would also like to thank Mário Levorato for providing the SRCC source code and Pedro Liguori for the helpful insights on the mathematical models.

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Authors and Affiliations

  1. Instituto de Computação, Universidade Federal Fluminense, Rua Passo da Pátria, São Domingos, 24210-240, Niterói-RJ, Brazil

    Eduardo Queiroga & Yuri Frota

  2. Departamento de Sistemas de Computação, Centro de Informática, Universidade Federal da Paraíba, Rua dos Escoteiros, Mangabeira, 58055-000, João Pessoa, Brazil

    Anand Subramanian

  3. Laboratoire Informatique d’Avignon, Avignon Université, 339 Chemin des Meinajaries, 84911, Avignon cedex 9, France

    Rosa Figueiredo

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  1. Eduardo Queiroga
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Correspondence to Eduardo Queiroga.

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Appendices

Appendix: Detailed results for the random RCC instances

Table 13 Relaxed imbalance obtained by ILS\(_\text {RCC}\) and ILS\(_\text {adapt}\)
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Table 14 Best solution of all experiments
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Detailed results for the SRCC instances

Table 15 Symmetric relaxed imbalance obtained by ILS\(_\text {RCC}\) and ILS Levorato et al. [36]
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Queiroga, E., Subramanian, A., Figueiredo, R. et al. Integer programming formulations and efficient local search for relaxed correlation clustering. J Glob Optim 81, 919–966 (2021). https://doi.org/10.1007/s10898-020-00989-7

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