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Detecting large risk-averse 2-clubs in graphs with random edge failures

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Abstract

Detecting large 2-clubs in biological, social and financial networks can help reveal important information about the structure of the underlying systems. In large-scale networks that are error-prone, the uncertainty associated with the existence of an edge between two vertices can be modeled by assigning a failure probability to that edge. Here, we study the problem of detecting large “risk-averse” 2-clubs in graphs subject to probabilistic edge failures. To achieve risk aversion, we first model the loss in 2-club property due to probabilistic edge failures as a function of the decision (chosen 2-club cluster) and randomness (graph structure). Then, we utilize the conditional value-at-risk (CVaR) of the loss for a given decision as a quantitative measure of risk for that decision, which is bounded in the model. More precisely, the problem is modeled as a CVaR-constrained single-stage stochastic program. The main contribution of this article is a new Benders decomposition algorithm that outperforms an existing decomposition approach on a test-bed of randomly generated instances, and real-life biological and social networks.

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Acknowledgments

Author Balasundaram would like to acknowledge the support of the Air Force Office of Scientific Research Grant FA9550-12-1-0103 and the National Science Foundation Grant CMMI-1404971. The computational experiments reported in this article were conducted at the Oklahoma State University High Performance Computing Center.

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Authors and Affiliations

  1. Management Science and Information Systems Department, University of Massachusetts Boston, Boston, MA, 02125, USA

    Foad Mahdavi Pajouh

  2. School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, 74078, USA

    Balabhaskar Balasundaram

  3. Lee Scott Logistics Complex, Wal-Mart Stores, Inc., 601 N Walton Blvd, Bentonville, AR, 72712, USA

    Esmaeel Moradi

Authors
  1. Foad Mahdavi Pajouh
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  2. Esmaeel Moradi
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  3. Balabhaskar Balasundaram
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Correspondence to Foad Mahdavi Pajouh.

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Mahdavi Pajouh, F., Moradi, E. & Balasundaram, B. Detecting large risk-averse 2-clubs in graphs with random edge failures. Ann Oper Res 249, 55–73 (2017). https://doi.org/10.1007/s10479-016-2279-0

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  • DOI: https://doi.org/10.1007/s10479-016-2279-0

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