A Partition-Based Heuristic for the Steiner Tree Problem in Large Graphs
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.
KeywordsSolution Quality Voronoi Diagram Memetic Algorithm Steiner Tree Problem Instance Graph
Unable to display preview. Download preview PDF.
- 4.Polzin, T.: Algorithms for the Steiner Problem in Networks. PhD thesis, Saarland University, Saarbrcken (2003)Google Scholar
- 6.Daneshmand, S.V.: Algorithmic Approaches to the Steiner Problem in Networks. PhD thesis, University of Mannheim, Mannheim (2003)Google Scholar
- 10.Uchoa, E., Werneck, R.F.F.: Fast local search for Steiner trees in graphs. In: Blelloch, G.E., Halperin, D. (eds.) ALENEX, pp. 1–10. SIAM (2010)Google Scholar
- 11.Luipersbeck, M.: A new partition-based heuristic for the Steiner tree problem in large graphs. Master’s thesis, Faculty of Informatics, Vienna University of Technology (December 2013)Google Scholar
- 13.Taillard, É.D., Voß, S.: POPMUSIC–Partial optimization metaheuristic under special intensification conditions. In: Essays and Surveys in Metaheuristics, pp. 613–629. Springer (2002)Google Scholar
- 18.Werneck, R.F.F.: Bossa (2003), http://www.cs.princeton.edu/~rwerneck/bossa/ (visited on January 20, 2014)
- 19.Koch, T., Martin, A., Voß, S.: SteinLib: An updated library on Steiner tree problems in graphs. Technical Report 00-37, ZIB, Takustr.7, 14195, Berlin (2000)Google Scholar
- 20.Leitner, M., Ljubić, I., Luipersbeck, M., Prossegger, M., Resch, M.: New real-world instances for the Steiner tree problem in graphs. Technical report, ISOR, University of Vienna (2014)Google Scholar