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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)

Abstract

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.

Keywords

Solution Quality Voronoi Diagram Memetic Algorithm Steiner Tree Problem Instance Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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