A Partition-Based Heuristic for the Steiner Tree Problem in Large Graphs

  • Markus Leitner
  • Ivana Ljubić
  • Martin Luipersbeck
  • Max Resch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8457)


This paper deals with a new heuristic for the Steiner tree problem (STP) in graphs which aims for the efficient construction of approximate solutions in very large graphs. The algorithm is based on a partitioning approach in which instances are divided into several subinstances that are small enough to be solved to optimality. A heuristic solution of the complete instance can then be constructed through the combination of the subinstances’ solutions. To this end, a new STP-specific partitioning scheme based on the concept of Voronoi diagrams is introduced. This partitioning scheme is then combined with state-of-the-art exact and heuristic methods for the STP. The implemented algorithms are also embedded into a memetic algorithm, which incorporates reduction tests, an algorithm for solution recombination and a variable neighborhood descent that uses best-performing neighborhood structures from the literature. All implemented algorithms are evaluated using previously existing benchmark instances and by using a set of new very large-scale real-world instances. The results show that our approach yields good quality solutions within relatively short time.


Solution Quality Voronoi Diagram Memetic Algorithm Steiner Tree Problem Instance Graph 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Markus Leitner
    • 1
  • Ivana Ljubić
    • 1
  • Martin Luipersbeck
    • 2
  • Max Resch
    • 2
  1. 1.Department of Statistics and Operations ResearchUniversity of ViennaViennaAustria
  2. 2.Vienna University of TechnologyAustria

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