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An exact solution framework for the minimum cost dominating tree problem

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Abstract

The minimum cost dominating tree problem is a recently introduced NP-hard problem, which consists of finding a tree of minimal cost in a given graph, such that for every node of the graph, the node or one of its neighbours is in the tree. We present an exact solution framework combining a primal–dual heuristic with a branch-and-cut approach based on a transformation of the problem into a Steiner arborescence problem with an additional constraint. The effectiveness of our approach is evaluated on testbeds proposed in literature containing instances with up to 500 nodes. Our framework manages to solve all but four instances from literature to proven optimality within 3 h (most of them in a few seconds). We provide optimal solution values for 69 instances from literature for which the optimal solution was previously unknown.

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Acknowledgements

E.A.-M. acknowledges the support of the Chilean Council of Scientific and Technological Research, CONICYT, through the Grant FONDECYT N.1180670 and through the Complex Engineering Systems Institute (ICM-FIC:P-05-004-F, CONICYT:FB0816). The research of M.S. was supported by the Austrian Research Fund (FWF, Project P 26755-N19). M.L. acknowledges the support of the University of Vienna through the uni:docs fellowship programme.

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Authors and Affiliations

  1. Department of Industrial Engineering, Universidad de Talca, Curicó, Chile

    Eduardo Álvarez-Miranda

  2. Department for Statistics and Operations Research, University of Vienna, Vienna, Austria

    Martin Luipersbeck

  3. Team INOCS, INRIA Lille-Nord Europe, Villeneuve d’Ascq, France

    Markus Sinnl

Authors
  1. Eduardo Álvarez-Miranda
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  2. Martin Luipersbeck
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  3. Markus Sinnl
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Correspondence to Eduardo Álvarez-Miranda.

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Álvarez-Miranda, E., Luipersbeck, M. & Sinnl, M. An exact solution framework for the minimum cost dominating tree problem. Optim Lett 12, 1669–1681 (2018). https://doi.org/10.1007/s11590-018-1252-z

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  • DOI: https://doi.org/10.1007/s11590-018-1252-z

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