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Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights

Author

Listed:
  • Maciej Rysz

    (National Research Council, Air Force Research Laboratory)

  • Foad Mahdavi Pajouh

    (University of Massachusetts Boston)

  • Pavlo Krokhmal

    (University of Arizona)

  • Eduardo L. Pasiliao

    (Air Force Research Laboratory)

Abstract

In this work, we study the problem of detecting risk-averse low-diameter clusters in graphs. It is assumed that the clusters represent k-clubs and that uncertain information manifests itself in the form of stochastic vertex weights whose joint distribution is known. The goal is to find a k-club of minimum risk contained in the graph. A stochastic programming framework that is based on the formalism of coherent risk measures is used to quantify the risk of a cluster. We show that the selected representation of risk guarantees that the optimal subgraphs are maximal clusters. A combinatorial branch-and-bound algorithm is proposed and its computational performance is compared with an equivalent mathematical programming approach for instances with $$k=2,3,$$ k = 2 , 3 , and 4.

Suggested Citation

  • Maciej Rysz & Foad Mahdavi Pajouh & Pavlo Krokhmal & Eduardo L. Pasiliao, 2018. "Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights," Annals of Operations Research, Springer, vol. 262(1), pages 89-108, March.
    • Handle: RePEc:spr:annopr:v:262:y:2018:i:1:d:10.1007_s10479-016-2212-6
    DOI: 10.1007/s10479-016-2212-6
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    References listed on IDEAS

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