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Stochastic and Risk Averse Maximum Subgraph Problems

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Encyclopedia of Optimization

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Abstract

This chapter summarizes recent advances in identifying subgraphs with given properties on stochastic graphs, which generalize the classical maximum subgraph problems such as the maximum clique problem. When the vertices of a graph have stochastic weights, a risk-averse stochastic optimization approach is described that allows one to find a subgraph with the lowest risk that also satisfies a prescribed graph-theoretic property. Similarly to deterministic maximum weight subgraphs problems, the minimum-risk subgraph is found among minimal subgraphs, i.e., such subgraphs whose order cannot be increased without breaking the desired property. In the case when the graph’s edges are stochastic, a two-stage stochastic programming approach is described for constructing or detecting “resilient” or “repairable” structures, or such sets of vertices that (i) induce a subgraph of a given property, and (ii) upon a randomized change of graph’s topology can be “repaired” via addition and/or deletion of vertices so as to restore the desired property, and whose cardinality is maximized. Exact combinatorial (graph-based) branch-and-bound algorithms for both types of models are presented.

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Authors and Affiliations

  1. Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ, USA

    Masoud Eshghali & Pavlo Krokhmal

  2. Department of Information Systems and Analytics, Miami University, Miami, FL, USA

    Maciej Rysz

Authors
  1. Masoud Eshghali
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  2. Maciej Rysz
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  3. Pavlo Krokhmal
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Corresponding author

Correspondence to Pavlo Krokhmal .

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Editors and Affiliations

  1. Department of Industrial & Systems Engin, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  2. Departmentl of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Oleg A. Prokopyev

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Eshghali, M., Rysz, M., Krokhmal, P. (2023). Stochastic and Risk Averse Maximum Subgraph Problems. In: Pardalos, P.M., Prokopyev, O.A. (eds) Encyclopedia of Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-54621-2_720-1

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  • DOI: https://doi.org/10.1007/978-3-030-54621-2_720-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-54621-2

  • Online ISBN: 978-3-030-54621-2

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

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