Mathematical Programming

, Volume 150, Issue 1, pp 49–78 | Cite as

The two-level diameter constrained spanning tree problem

  • Luis Gouveia
  • Markus LeitnerEmail author
  • Ivana Ljubić
Full Length Paper Series B


In this article, we introduce the two-level diameter constrained spanning tree problem (2-DMSTP), which generalizes the classical DMSTP by considering two sets of nodes with different latency requirements. We first observe that any feasible solution to the 2-DMSTP can be viewed as a DMST that contains a diameter constrained Steiner tree. This observation allows us to prove graph theoretical properties related to the centers of each tree which are then exploited to develop mixed integer programming formulations, valid inequalities, and symmetry breaking constraints. In particular, we propose a novel modeling approach based on a three-dimensional layered graph. In an extensive computational study we show that a branch-and-cut algorithm based on the latter model is highly effective in practice.


Networks/graphs: tree algorithms Integer programming: formulations Layered graphs 

Mathematics Subject Classification (2000)

90C11 90C27 90C57 


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014

Authors and Affiliations

  1. 1.Faculdade de CiênçiasUniversidade de LisboaLisbonPortugal
  2. 2.Department of Statistics and Operations ResearchUniversity of ViennaViennaAustria
  3. 3.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

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