Effective Local Search Techniques for the Steiner Tree Problem

  • A. S. C. Wade
  • V. J. Rayward-Smith
Part of the Combinatorial Optimization book series (COOP, volume 6)


Steiner’s Problem in Graphs (SPG) involves connecting a given subset of a graph’s vertices as cheaply as possible. More precisely, given a graph G = (V, E) with vertices V, edges E, a cost function c: EZ +, and a set of special vertices, KV, a Steiner tree is a connected subgraph, T = (V T , E T ), such that KV T V and |E| T =|V T |-1. The problem is to find a Steiner tree T which minimises the cost function, Such a tree is referred to as a minimal Steiner tree.


Local Search Minimum Span Tree Steiner Tree Local Search Algorithm Steiner Tree Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J.E. Beasley. An SST-based algorithm for the Steiner problem in graphs. Networks, 19:1–16, 1989.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    J.E. Beasley. OR-Library: Distributing test problems by electronic mail. Journal of the Operations Research Society, 41:1069–1072, 1990.Google Scholar
  3. [3]
    S. Chopra, E.R. Gorres, and M.R. Rao. Solving the Steiner tree problem on a graph using branch and cut. ORSA Journal on Computing, 4(3):320–335,1992.MATHCrossRefGoogle Scholar
  4. [4]
    E.W. Dijkstra. A note on two problems in connexion with graphs. Numerische Math., 1:269–271, 1959.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Kathryn A. Dowsland. Hill-climbing, Simulated Annealing and the Steiner problem in graphs. Engineering Optimization, 17:91–107, 1991.CrossRefGoogle Scholar
  6. [6]
    C.W. Duin and A. Volgenant. Reduction tests for the Steiner problem in graphs. Networks, 19:549–567, 1989.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    S.E. Dreyfus and R.A. Wagner. The Steiner problem in graphs. Networks, 1:195–207, 1971.MathSciNetCrossRefGoogle Scholar
  8. [8]
    H. Esbensen. Computing near-optimal solutions to the Steiner problem in a graph using a genetic algorithm. Networks, 26:173–185, 1995.MATHCrossRefGoogle Scholar
  9. [9]
    S.L. Hakimi. Steiner’s problem in graphs and its applications. Networks, 1:113–133, 1971.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    R. M. Karp. Reducibility among combinatorial problems. In R.E. Miller and J.W. Thatcher, editors, Complexity of Computer Computations, pages 85–103. Plenum Press, 1972.CrossRefGoogle Scholar
  11. [11]
    L. Kou, G. Markowsky, and L. Berman. A fast algorithm for Steiner trees. Acta Informatica, 15:141–145, 1981.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    A. Kapsalis, V.J. Rayward-Smith, and G.D. Smith. Solving the graphical Steiner tree problem using genetic algorithms. J. Oper. Res. Soc., 44:397–406, 1993.MATHGoogle Scholar
  13. [13]
    S. Lin and B.W. Kernighan. An effective heuristic algorithm for the Traveling Salesman Problem. Operations Research, 21:498–516, 1973.MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    B.M.E. Moret and H.D. Shapiro. Algorithms from P to NP. Volume I: Design and Efficiency. Benjamin-Cummings, Menlo Park, CA, 1991.Google Scholar
  15. [15]
    L. Osborne and B. Gillett. A comparison of two Simulated Annealing algorithms applied to the directed Steiner problem on networks. ORSA Journal on Computing, 3(3):213–225,1991.MATHCrossRefGoogle Scholar
  16. [16]
    V.J. Rayward-Smith and A. Clare. On finding Steiner vertices. Networks, 16:283–294, 1986.MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    P.M. Spira. On finding and updating spanning trees and shortest paths. SIAM Journal on Computing, 4:375–380, 1975.MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    H. Takahashi and A. Matsuyama. An approximate solution for the Steiner problem in graphs. Mathematica Japonica, 24:573–577, 1980.MathSciNetMATHGoogle Scholar
  19. [19]
    M.G.A. Verhoeven, E.H.L. Aarts, and M.E.M. Severens. Local search for the Steiner problem in graphs. In V.J. Rayward-Smith, editor, Modern Heuristic Search Methods. J. Wiley, 1996.Google Scholar
  20. [20]
    M Yannakakis. The analysis of local search problems and their heuristics. In Proceedings of the seventh Symposium on Theoretical Aspects of Computer Science, volume LNCS 415, pages 298–311, Berlin, 1990. Springer-Verlag.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • A. S. C. Wade
    • 1
  • V. J. Rayward-Smith
    • 1
  1. 1.School of Information SystemsUniversity of East AngliaNorwichUK

Personalised recommendations