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Determining a Minimum Spanning Tree with Disjunctive Constraints

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Book cover Algorithmic Decision Theory (ADT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5783))

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Abstract

For the classical minimum spanning tree problem we introduce disjunctive constraints for pairs of edges which can not be both included in the spanning tree at the same time. These constraints are represented by a conflict graph whose vertices correspond to the edges of the original graph. Edges in the conflict graph connect conflicting edges of the original graph. It is shown that the problem becomes strongly \(\mathcal{NP}\)-hard even if the connected components of the conflict graph consist only of paths of length two. On the other hand, for conflict graphs consisting of disjoint edges (i.e. paths of length one) the problem remains polynomially solvable.

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Author information

Authors and Affiliations

  1. Institute of Public Economics, University of Graz, Universitaetsstr, 15, 8010, Graz, Austria

    Andreas Darmann

  2. Department of Statistics and Operations Research, University of Graz, Universitaetsstr, 15, 8010, Graz, Austria

    Ulrich Pferschy & Joachim Schauer

Authors
  1. Andreas Darmann
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  2. Ulrich Pferschy
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  3. Joachim Schauer
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Editor information

Editors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Padova, Via Trieste 63, 35121, Padova, Italy

    Francesca Rossi

  2. LAMSADE-CNRS, University of Paris Dauphine, Place du Maréchal De Lattre de Tassigny, 75775, Paris Cedex 16, France

    Alexis Tsoukias

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© 2009 Springer-Verlag Berlin Heidelberg

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Darmann, A., Pferschy, U., Schauer, J. (2009). Determining a Minimum Spanning Tree with Disjunctive Constraints. In: Rossi, F., Tsoukias, A. (eds) Algorithmic Decision Theory. ADT 2009. Lecture Notes in Computer Science(), vol 5783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04428-1_36

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  • DOI: https://doi.org/10.1007/978-3-642-04428-1_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04427-4

  • Online ISBN: 978-3-642-04428-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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