Exact approaches for the directed network design problem with relays

M. Leitner, Ivana Ljubic, Mario Ruthmair, Martin Riedler

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We study the directed network design problem with relays (DNDPR) whose aim is to construct a minimum cost network that enables the communication of a given set of origin-destination pairs. Thereby, expensive signal regeneration devices need to be placed to cover communication distances exceeding a predefined threshold. Applications of the DNDPR arise in telecommunications and transportation. We propose two new integer programming formulations for the DNDPR. The first one is a flow-based formulation with a pseudo-polynomial number of variables and constraints and the second is a cut-based formulation with an exponential number of constraints. Fractional distance values are handled efficiently by augmenting both models with an exponentially-sized set of infeasible path constraints. We develop branch-and-cut algorithms and also consider valid inequalities to strengthen the obtained dual bounds and to speed up convergence. The results of our extensive computational study on diverse sets of benchmark instances show that our algorithms outperform the previous state-of-the-art method based on column generation.
Original languageEnglish
Article number102005
Pages (from-to)1-17
Number of pages17
Early online date16 Nov 2018
Publication statusPublished - Mar 2020


  • Integer Programming
  • Layered Graphs
  • Networks
  • Telecommunications


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