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A branch-and-bound approach for maximum quasi-cliques

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Abstract

Detecting quasi-cliques in graphs is a useful tool for detecting dense clusters in graph-based data mining. Particularly in large-scale data sets that are error-prone, cliques are overly restrictive and impractical. Quasi-clique detection has been accomplished using heuristic approaches in various applications of graph-based data mining in protein interaction networks, gene co-expression networks, and telecommunication networks. Quasi-cliques are not hereditary, in the sense that every subset of a quasi-clique need not be a quasi-clique. This lack of heredity introduces interesting challenges in the development of exact algorithms to detect maximum cardinality quasi-cliques. The only exact approaches for this problem are limited to two mixed integer programming formulations that were recently proposed in the literature. The main contribution of this article is a new combinatorial branch-and-bound algorithm for the maximum quasi-clique problem.

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Acknowledgements

The authors would like to thank the two anonymous referees for their comments that improved the content and presentation of this article, and would also like to thank Dr. Sergiy Butenko for sharing the manuscript of Patillo et al. (2012) with us. The computational experiments reported in this article were performed at the Oklahoma State University High Performance Computing Center (OSUHPCC). The authors are grateful to Dr. Dana Brunson for her support in conducting these experiments at OSUHPCC. This research was supported by the US Department of Energy Grant DE-SC0002051 and the Air Force Office of Scientific Research Grant FA9550-12-1-0103.

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  1. School of Industrial Engineering & Management, Oklahoma State University, Stillwater, OK, 74078, USA

    Foad Mahdavi Pajouh, Zhuqi Miao & Balabhaskar Balasundaram

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  1. Foad Mahdavi Pajouh
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  2. Zhuqi Miao
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  3. Balabhaskar Balasundaram
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Correspondence to Balabhaskar Balasundaram.

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Mahdavi Pajouh, F., Miao, Z. & Balasundaram, B. A branch-and-bound approach for maximum quasi-cliques. Ann Oper Res 216, 145–161 (2014). https://doi.org/10.1007/s10479-012-1242-y

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