Skip to main content
Springer Nature Link
Log in

An exact branch and bound algorithm for the Steiner Problem in Graphs

  • Session 10B: Algorithms
  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 959))

Included in the following conference series:

  • 185 Accesses

Abstract

An exact branch and bound algorithm for the Steiner Problem in Graphs (SPG) is presented, based on a new integer programming formulation. The algorithm proves to be robust and relatively efficient based on preliminary results obtained for average-size problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Balakrishnan, A., and N. R. Patel. Problem reduction methods and a tree generation algorithm for the Steiner network problem. Networks, 17:65–85, 1987.

    Google Scholar 

  2. Beasley, J. E. An SST-based algorithm for the Steiner problem on graphs. Networks, 19:1–16, 1989.

    Google Scholar 

  3. J. E. Beasley, OR-Library: Distributing test problems by electronic mail. J. of Oper. Res. Soc. 41(11) (1990) 1069–1072.

    Google Scholar 

  4. Beasley, J. E.. A heuristic for the Euclidean and rectilinear Steiner problems. Europ. J. of Oper. Res., 58:284–292, 1992.

    Article  Google Scholar 

  5. Chopra, S., E. R. Gorres, and M. R. Rao. Solving the Steiner tree problem on graphs using branch and cut. ORSA Journal on Computing, 4(3):320–335, 1992.

    Google Scholar 

  6. S. L. Hakimi, Steiner's problem in graphs and its implications. Networks 1 (1971) 113–133.

    Google Scholar 

  7. F. K. Hwang, D. S. Richards and P. Winter, The Steiner Tree Problem, Elsevier, Amsterdam (1992).

    Google Scholar 

  8. B. N. Khoury and P. M. Pardalos, A Heuristic for the Steiner Problem in Graphs. Computational Optimization and Applications, (1995).

    Google Scholar 

  9. B. N. Khoury, P. M. Pardalos and D.-Z. Du, A test problem generator for the Steiner problem in graphs. ACM Transactions on Mathematical Software, Vol. 19, No. 4 (1993), pp. 509–522.

    Article  Google Scholar 

  10. B. N. Khoury, P. M. Pardalos and D. W. Hearn, Equivalent formulations for the Steiner problem in graphs. In Network Optimization Problems, 111–124, P.M. Pardalos and D.-Z. Du (Eds.), World Scientific (1993).

    Google Scholar 

  11. J. MacGregor Smith and P. Winter (Eds.), Topological Network Design Vol. 31(1–4) of Annals of Operations Research (1991)

    Google Scholar 

  12. Murtagh, B. A., and M. A. Saunders. MINOS 5.4 user's guide(preliminary). Technical Report SOL 83-20R, Department of Operations Research, Stanford University, Stanford, CA, 1983.

    Google Scholar 

  13. Shore, M. L., L. R. Foulds, and P. B. Gibbons. An algorithm for the Steiner problem in graphs. Networks, 12:323–333, 1982.

    Google Scholar 

  14. J. Soukup and W. F. Chow, Set of test problems for the minimum length connection networks. ACM/SIGMAP Newsletter 15 (1973) 48–51.

    Google Scholar 

  15. S. Voss, Steiner-Probleme in Graphen [in German], Hain, Frankfurt (1990).

    Google Scholar 

  16. Yang, Y. Y., and O. Wing. An algorithm for the wiring problem. Digest Ieee Int. Symp. Electrical Networks, 14–15, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Applied Optimization and ISE Department, University of Florida, 303 Weil Hall, 32611, Gainesville, Florida

    B. N. Khoury & P. M. Pardalos

Authors
  1. B. N. Khoury
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ding-Zhu Du Ming Li

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Khoury, B.N., Pardalos, P.M. (1995). An exact branch and bound algorithm for the Steiner Problem in Graphs. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030880

Download citation

  • DOI: https://doi.org/10.1007/BFb0030880

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60216-3

  • Online ISBN: 978-3-540-44733-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics