Correct and provably efficient methods for rectilinear Steiner spanning tree generation

  • F. D. Lewis
  • N. Van Cleave
Track 9: VLSI Design
Part of the Lecture Notes in Computer Science book series (LNCS, volume 507)


Two rectilinear Steiner spanning tree algorithms are presented, proven to be correct, and examined with regard to their complexity. It is shown that their worst case efficiencies are merely 1.5 times the optimum solution. These algorithms, when experimentally compared to existing algorithms, excel. They in fact produce the best solutions over 80% of the time and are never more than 1% from the best solution found.


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6. References

  1. BC85.
    Bern, M. W., and M. de Carvalho. “A Greedy Hueristic for the Rectilinear Steiner Tree Problem.” Univ. California at Berkeley TR, (1985).Google Scholar
  2. GaJo77.
    Garey, M. R., and D. S. Johnson. “The Rectilinear Steiner Tree Problem is NP-Complete.” SIAM J of Applied Mathematics, 32 (1977), 855–859.Google Scholar
  3. Ha66.
    Hanan, M. “On Steiners Problem with Rectilinear Distance.” SIAM Journal of Applied Mathematics, 14:2 (1966), 255–265.zbMATHMathSciNetCrossRefGoogle Scholar
  4. HVW89.
    Ho, J., G. Vijayan, and C. K. Wong. “A New Approach to the Steiner Tree Problem.” Proc. 26th ACM/IEEE Design Auto. Conf. (1989), 161–166.Google Scholar
  5. Hw76.
    Hwang, F. K. “On Steiner Minimal Trees with Rectilinear Distance.” SIAM Journal of Applied Mathematics, 30 (1976), 104–114.zbMATHCrossRefGoogle Scholar
  6. Hw79.
    Hwang, F. K. “An O(nlogn) Algorithm for Sub-optimal Rectilinear Steiner Trees.” IEEE Trans. on Circuits and Systems CAS-26:1 (1979), 75–77.CrossRefGoogle Scholar
  7. ImAs86.
    Imai, H., and T. Asano. “Efficient Algorithms for Geometric Graph Search Problems.” SIAM Journal of Computing, 15:2 (1986), 478–494.zbMATHMathSciNetCrossRefGoogle Scholar
  8. KoSh85.
    Komlos, J., and M. T. Shing. “Probabilistic Partitioning Algorithms for the Rectilinear Steiner Problem.” Network, 15 (1985), 413–423.zbMATHMathSciNetGoogle Scholar
  9. Kr56.
    Kruskal, J. B. “On the Shortest Spanning Subtree of a Graph.” Proceedings of the American Mathematical Society, 7 (1956) 48–50.zbMATHMathSciNetCrossRefGoogle Scholar
  10. LaLi81.
    Larson, R. C., and V. O. Li. “Finding Minimum Rectilinear Distance Paths in the Presence of Barriers.” Networks, 11 (1981), 285–304.zbMATHMathSciNetGoogle Scholar
  11. LBH76.
    Lee, J. H., N. K. Bose, and F. K. Hwang. “Use of Steiner's Problem in Suboptimal Routing in Rectilinear Metric.” IEEE Trans. on Circuits and Systems, CAS-23:7 (July 1976), 470–476.MathSciNetCrossRefGoogle Scholar
  12. LiMa84.
    Li, J. T., and M. Marek-Sadowska. “Global Routing for Gate Arrays.” IEEE Trans. on Computer Aided Design of Integrated Circuits and Systems, CAD-3:4 (Oct 1984), 298–308.Google Scholar
  13. NRT86.
    Ng, A. P-C, P. Raghavan, and C. D. Thompson. “Experimental Results for a Linear Program Global Router.” manuscript submitted to: Computers and AI and 1986 ACM Design Automation Conference, (November 1985).Google Scholar
  14. Pr57.
    Prim, R. C. “Shortest Connection Networks and Some Generalizations.” Bell System Tech. J. 36 (1957), 1389–1401.Google Scholar
  15. Ra83.
    Rayward-Smith, V.J. “The Computation of Nearly Minimal Steiner Trees in Graphs.” Int. J. of Math. Education in Sci. and Tech. 14 (1983), 15–23.zbMATHMathSciNetGoogle Scholar
  16. Ri89.
    Richards, D. “Fast Heuristic Algorithms for Rectilinear Steiner Trees.” Algorithmica 4 (1989), 191–207.zbMATHMathSciNetCrossRefGoogle Scholar
  17. SLL80.
    Smith, J. M., D. T. Lee, and J. S. Liebman. “An O(nlogn) Heuristic Algorithm for the Rectilinear Steiner Minimal Tree Problem.” Eng. Optimization 4 (1980), 179–192.Google Scholar
  18. TM80.
    Takahashi, H. and A Matsuyama. “An Approximate Solution for the Steiner Problem in Graphs.” Mathematica Japonica 24 (1980), 573–577.zbMATHMathSciNetGoogle Scholar
  19. Va87.
    Van Cleave, N. “Rectilinear Steiner Tree Algorithms for the Global Routing Phase of VLSI Design.” M.S. Thesis, University of Kentucky, Lexington, KY (1987).Google Scholar
  20. VeKi83.
    Vecchi, M., and S. Kirkpatrick. “Global Wiring by Simulated Annealing.” IEEE Trans. on Computer-Aided Design,” CAD-2:4 (Oct 1983), 215–222.CrossRefGoogle Scholar
  21. Wi87.
    Winter, P. “Steiner Problem in Networks: A Survey.” Networks, 17 (1987), 128–167.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • F. D. Lewis
    • 1
  • N. Van Cleave
    • 1
  1. 1.University of KentuckyUSA

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