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The Maximum Weight Connected Subgraph Problem

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Facets of Combinatorial Optimization

Abstract

The Maximum (Node-) Weight Connected Subgraph Problem (MWCS) searches for a connected subgraph with maximum total weight in a node-weighted (di)graph. In this work we introduce a new integer linear programming formulation built on node variables only, which uses new constraints based on node-separators. We theoretically compare its strength to previously used MIP models in the literature and study the connected subgraph polytope associated with our new formulation. In our computational study we compare branch-and-cut implementations of the new model with two models recently proposed in the literature: one of them using the transformation into the Prize-Collecting Steiner Tree problem, and the other one working on the space of node variables only. The obtained results indicate that the new formulation outperforms the previous ones in terms of the running time and in terms of the stability with respect to variations of node weights.

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Acknowledgements

We are deeply thankful to Christina Backes from the Department of Human Genetics, Saarland University, who helped in the understanding and interpretation of the regulatory network instances considered in this paper. This research is partially conducted during the research stay of Ivana Ljubić at the TU Dortmund, supported by the APART Fellowship of the Austrian Academy of Sciences. This support is greatly acknowledged. Eduardo Álvarez-Miranda thanks the Institute of Advanced Studies of the Università di Bologna from where he is a Ph.D. Fellow.

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Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Energia Elettrica e dell’Informazione, Università di Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

    Eduardo Álvarez-Miranda

  2. Institut für Statistik und Operations Research, Universität Wien, Brünnerstraße 72, 1210, Vienna, Austria

    Ivana Ljubić

  3. Fakultät für Informatik, Technische Universität Dortmund, Otto-Hahn-Straße 14, 44227, Dortmund, Germany

    Petra Mutzel

Authors
  1. Eduardo Álvarez-Miranda
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  2. Ivana Ljubić
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  3. Petra Mutzel
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Correspondence to Ivana Ljubić .

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Editors and Affiliations

  1. Dept. of Computer Science, University of Cologne, Pohligstr. 1, Cologne, 50969, Germany

    Michael Jünger

  2. Dept. of Computer Science, University of Heidelberg, Im Neuenheimer Feld 326, Heidelberg, 69120, Germany

    Gerhard Reinelt

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Álvarez-Miranda, E., Ljubić, I., Mutzel, P. (2013). The Maximum Weight Connected Subgraph Problem. In: Jünger, M., Reinelt, G. (eds) Facets of Combinatorial Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38189-8_11

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