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Parametric analysis on cut-trees and its application on a protein clustering problem

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Abstract

Computing the maximum flow value between a pair of nodes in a given network is a classic problem in the context of network flows. Its extension, namely, the multi-terminal maximum flow problem, comprises finding the maximum flow values between all pairs of nodes in a given undirected network. In this work, we provide an overview of the recent theory of sensitivity analysis, which examines the influence of a single edge capacity variation on the multi-terminal maximum flows, and we make remarks about extending some theoretical results to the case where more than one edge has their capacities changed. Based on these extensions, we present algorithms to construct the Gomory and Hu cut-trees dynamically, considering capacity variations in more than one edge in the network. Finally, the presented theory is applied on a clustering problem, in the field of biology, in order to improve an existing algorithm that identifies protein complexes in protein–protein interaction networks. In this application, a new result in the sensitivity analysis theory is introduced.

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Authors and Affiliations

  1. Departamento de Engenharia Industrial, PUC-Rio, Rua Marquês de São Vicente, 225, Gávea, Rio de Janeiro, RJ, 22451-900, Brazil

    João Paulo de Freitas Araujo, Madiagne Diallo & José Eugenio Leal

  2. Laboratório Nacional de Computação Científica, Av. Getúlio Vargas, 333, Quitandinha, Petrópolis, RJ, CEP 25651-075, Brazil

    Fernanda Maria Pereira Raupp

  3. INSA Centre Val de Loire, 88 Boulevard Lahitolle, 60013 – 18022, Bourges Cedex, France

    Pascal Berthomé

Authors
  1. João Paulo de Freitas Araujo
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  2. Madiagne Diallo
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  3. Fernanda Maria Pereira Raupp
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  4. Pascal Berthomé
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  5. José Eugenio Leal
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Correspondence to João Paulo de Freitas Araujo.

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de Freitas Araujo, J.P., Diallo, M., Pereira Raupp, F.M. et al. Parametric analysis on cut-trees and its application on a protein clustering problem. Cent Eur J Oper Res 28, 229–249 (2020). https://doi.org/10.1007/s10100-018-0579-y

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  • DOI: https://doi.org/10.1007/s10100-018-0579-y

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