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Computational Complexities of Optimization Problems Related to Model-Based Clustering of Networks

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Optimization in Science and Engineering

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Abstract

An extremely popular model-based graph partitioning approach that is used for both biological and social networks is the so-called modularity optimization approach originally proposed by Newman and its variations. In this chapter, we review several combinatorial and algebraic methods that have been used in the literature to study the computational complexities of these optimization problems.

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Notes

  1. 1.

    The definitions can be easily generalized for directed and weighted graphs; see Sect. 3.5.

  2. 2.

    Each V i is usually called a “cluster”.

  3. 3.

    See [48, part II] for further details of such an approach.

  4. 4.

    See [48, Chap. 26].

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Acknowledgments

The author was supported by NSF grant IIS-1160995.

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Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Chicago, Chicago, IL, 50507, USA

    Bhaskar DasGupta

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  1. Bhaskar DasGupta
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Correspondence to Bhaskar DasGupta .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Princeton University Dept. Chemical Engineering, Princeton, New Jersey, USA

    Christodoulos A. Floudas

  3. Dept. Industrial & Systems Engineering, Texas A&M University, College Station, Texas, USA

    Sergiy Butenko

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DasGupta, B. (2014). Computational Complexities of Optimization Problems Related to Model-Based Clustering of Networks. In: Rassias, T., Floudas, C., Butenko, S. (eds) Optimization in Science and Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0808-0_5

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