Skip to main content
Log in

Comparison of formulations and a heuristic for packing Steiner trees in a graph

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

In this paper, we consider the problem of packing Steiner trees in a graph. This problem arises during the global routing phase of circuit layout design. We consider various integer programming formulations and rank them according to lower bounds they provide as LP-relaxations. We discuss a solution procedure to obtain both lower and upper bounds using one of the LP-relaxations. Computational results to test the effectiveness of our procedures are provided.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J.E. Beasley, An SST-based algorithm for the Steiner Tree problem in graphs, Networks 19(1989)1–16.

    Google Scholar 

  2. S. Chopra, E. Gorres and M.R. Rao, Solving the Steiner Tree problem on a graph using branch and cut, ORSA J. Comp. 4(1992)320–335.

    Google Scholar 

  3. M.L. Fisher, The Lagrangian relaxation method for solving integer programming problems, Manag. Sci. 27(1981)1–18.

    Google Scholar 

  4. L.R. Ford, Jr. and D.R. Fulkerson,Flows in Networks (Princeton University Press, Princeton, NJ, 1962).

    Google Scholar 

  5. M. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979).

    Google Scholar 

  6. M. Grötschel, L. Lovasz and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica 1(1981)169–191.

    Google Scholar 

  7. M. Grötschel, A. Martin and R. Weismantel, Packing Steiner trees: Polyhedral investigations, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Preprint SC 92-8 (1992).

  8. M. Grötschel, A. Martin and R. Weismantel, Packing Steiner tress: A cutting plane algorithm and computational results, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Preprint SC 92-9 (1992).

  9. C.Y. Lee, An algorithm for path connection and its applications, IRE Trans. Electron. Comp. EC-10(1961)346–365.

    Google Scholar 

  10. T. Lengauer,Combinatorial Algorithms for Integrated Circuit Layout (Wiley, 1990).

  11. T. Lengauer and M. Lügering, Integer program formulations of global routing and placement problems, Research Report, University of Paderborn, Germany.

  12. B. Korte, H.J. Prömel and A. Steger, Steiner trees in VLSI layout, in:Paths, Flows, and VLSI-Layout, ed. B. Korte, L. Lovasz, H.J. Prömel and A. Schrijver (Springer, 1990).

  13. A. Martin, Packen von Steinerbäumen: Polyredrische Studien und Anwendung, Ph.D. Thesis, Technische Universität Berlin (1992).

  14. E.F. Moore, Shortest path through a maze, in:Proc. Int. Symp. on Switching Circuits (Harvard University Press, 1959) pp. 285–292.

  15. A.P.C. Ng, P. Raghavan and C.D. Thompson, Experimental results for a linear program global router, Comp. Art. Int. 6(1987)229–242.

    Google Scholar 

  16. P. Raghavan and C.D. Thompson, Randomized rounding: A technique for provably good algorithms and algorithmic proofs, Combinatorica 7(1987)365–374.

    Google Scholar 

  17. M.B. Richey and R.G. Parker, On multiple Steiner subgraph problems, Networks 16(1986)423–438.

    Google Scholar 

  18. H. Takahashi and A. Matsuyama, An approximate solution for the Steiner problem in graphs, Math. Japonica 24(1980)573–577.

    Google Scholar 

  19. R.T. Wong, A dual ascent approach for Steiner Tree problems on a directed graph, Math. Progr. 28(1984)271–287.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chopra, S. Comparison of formulations and a heuristic for packing Steiner trees in a graph. Ann Oper Res 50, 143–171 (1994). https://doi.org/10.1007/BF02085638

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02085638

Keywords

Navigation