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Maximizing Barber’s bipartite modularity is also hard

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Abstract

Modularity introduced by Newman and Girvan (Phys Rev E 69:026113, 2004) is a quality function for community detection in networks. Numerous methods for modularity maximization have been developed so far. In 2007, Barber (Phys Rev E 76:066102, 2007) introduced a variant of modularity called bipartite modularity which is appropriate for bipartite networks. Although maximizing the standard modularity is known to be NP-hard, the computational complexity of maximizing bipartite modularity has yet to be revealed. In this study, we prove that maximizing bipartite modularity is also NP-hard. More specifically, we show the NP-completeness of its decision version by constructing a reduction from a classical partitioning problem.

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Acknowledgments

The authors would like to thank the anonymous referee for helpful comments. The authors are supported by the Grant-in-Aid for JSPS Fellows.

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Authors and Affiliations

  1. Graduate School of Decision Science and Technology, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8552, Japan

    Atsushi Miyauchi & Noriyoshi Sukegawa

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  1. Atsushi Miyauchi
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  2. Noriyoshi Sukegawa
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Correspondence to Atsushi Miyauchi.

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Miyauchi, A., Sukegawa, N. Maximizing Barber’s bipartite modularity is also hard. Optim Lett 9, 897–913 (2015). https://doi.org/10.1007/s11590-014-0818-7

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  • DOI: https://doi.org/10.1007/s11590-014-0818-7

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