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Orientation-based models for {0,1,2}-survivable network design: theory and practice

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Abstract

We consider {0,1,2}-Survivable Network Design problems with node-connectivity constraints. In the most prominent variant, we are given an edge-weighted graph and two customer sets \({\fancyscript{R}_1}\) and \({\fancyscript{R}_2}\) ; we ask for a minimum cost subgraph that connects all customers, and guarantees two-node-connectivity for the \({\fancyscript{R}_2}\) customers. We also consider an alternative of this problem, in which 2-node-connectivity is only required w.r.t. a certain root node, and its prize-collecting variant. The central result of this paper is a novel graph-theoretical characterization of 2-node-connected graphs via orientation properties. This allows us to derive two classes of ILP formulations based on directed graphs, one using multi-commodity flow and one using cut-inequalities. We prove the theoretical advantages of these directed models compared to the previously known ILP approaches. We show that our two concepts are equivalent from the polyhedral point of view. On the other hand, our experimental study shows that the cut formulation is much more powerful in practice. Moreover, we propose a collection of benchmark instances that can be used for further research on this topic.

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Authors and Affiliations

  1. Chair XI Algorithm Engineering, TU Dortmund, Otto-Hahn-Str. 14, 44227, Dortmund, Germany

    Markus Chimani, Maria Kandyba & Petra Mutzel

  2. Department of Statistics and Decision Support Systems, University of Vienna, Brünnerstr. 72, 1210, Vienna, Austria

    Ivana Ljubić

Authors
  1. Markus Chimani
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  2. Maria Kandyba
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  3. Ivana Ljubić
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  4. Petra Mutzel
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Corresponding author

Correspondence to Markus Chimani.

Additional information

Preliminary parts of this paper appeared at ESA 2007 and COCOA 2008. M. Kandyba was supported by the German Research Foundation (DFG) through the Collaborative Research Center “Computational Intelligence” (SFB 531). I. Ljubić was supported by the Hertha-Firnberg Fellowship of the Austrian Science Foundation (FWF). P. Mutzel was partially supported by the Austrian Research Promotion Agency (FFG) under grant 811378 (NetQuest project).

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Chimani, M., Kandyba, M., Ljubić, I. et al. Orientation-based models for {0,1,2}-survivable network design: theory and practice. Math. Program. 124, 413–439 (2010). https://doi.org/10.1007/s10107-010-0375-5

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  • DOI: https://doi.org/10.1007/s10107-010-0375-5

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