The minimal Steiner tree problem is a classical NP-complete problem that has several applications in the communication and transportation sectors. It has recently emerged as a subproblem in decomposition techniques such as column generation and Lagrangian schemes. This has set new computational challenges to the state of the art solving approaches. Our goal is to improve on existing branch-and-cut algorithms so that our approach successfully serves as a fast subproblem solver in a decomposition context. Compared with existing literature, our technical contributions include 1) a new preflow-push cutting strategy, revisiting a little known graph algorithm, that halves the runtime of the separation step, and 2) a branching scheme that fairly balances the search tree and speeds up the search. An evaluation in a multicast design application shows that the algorithm enhances a column generation hybrid. Moreover, our approach offers a significant speedup factor on a publicly available set of challenging Steiner tree benchmarks.


networks preflow-push algorithms branch-and-cut Steiner trees 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Wilhelm Cronholm
    • 1
  • Farid Ajili
    • 1
  • Sofia Panagiotidi
    • 2
  1. 1.IC-ParcImperial College LondonLondonUK
  2. 2.London e-Science CentreImperial College LondonLondonUK

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