A New Heuristic for Rectilinear Steiner Trees

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Volumn 19, Issue 10, 2000, Pages 1129-1139

  Mǎndoiu, Ion I ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

Interconnect synthesis; Optimization; Routing; Steiner tree

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER AIDED DESIGN; GRAPH THEORY; HEURISTIC METHODS; INTEGER PROGRAMMING; INTEGRATED CIRCUIT TESTING; LINEAR PROGRAMMING; RANDOM PROCESSES; VLSI CIRCUITS;

APPROXIMATION ALGORITHMS; GEOSTEINER CODE; INTERCONNECT SYNTHESIS; RECTILINEAR STEINER TREES;

INTEGRATED CIRCUIT LAYOUT;

EID: 0034292748     PISSN: 02780070     EISSN: None     Source Type: Journal    
DOI: 10.1109/43.875292     Document Type: Article

References (31)

1. M. R. Garey and D. S. Johnson, "The rectilinear Steiner tree problem is NP-complete," SIAM J. Appl. Math., vol. 32, pp. 826-834, 1977.
2. A. Agrawal, P. Klein, and R. Ravi, "When trees collide: An approximation algorithm for the generalized Steiner problem in networks," SIAM J. Comput., vol. 24, pp. 440-456, 1995.
3. P. Berman and V. Ramaiyer, "Improved approximations for the Steiner tree problem," J. Algorithms, vol. 17, pp. 381-408, 1994.
4. M. Borah, R. M. Owens, and M. J. Irwin, "A fast and simple Steiner routing heuristic," Discret. Appl. Math., vol. 90, pp. 51-67, 1999.
5. U. Fößmeier, M. Kaufmann, and A. Z. Zelikovsky, "Faster approximation algorithms for the rectilinear Steiner tree problem," Discret. Comput. Geometry, vol. 18, pp. 93-109, 1997.
6. M. X. Goemans and D. P. Williamson, "A general approximation technique for constrained forest problems," SIAM J. Comput., vol. 24, pp. 296-317, 1995.
7. J. Ho, G. Vijayan, and C. K. Wong, "New algorithms for the rectilinear Steiner tree problem," IEEE Trans. Computer-Aided Design, vol. 9, pp. 185-193, Feb. 1990.
8. F. K. Hwang, "An O(n log n) algorithm for rectilinear Steiner trees," IEEE Trans. Circuits Syst., vol. 26, pp. 75-77, Jan. 1979.
9. A. B. Kahng and G. Robins, "A new class of iterative Steiner tree heuristics with good performance," IEEE Trans. Computer-Aided Design, vol. 11, pp. 893-902, July 1992.
10. F. D. Lewis, W. C.-C. Pong, and N. Van Cleave, "Local improvement in Steiner trees," in Proc. 3rd Great Lakes Symp. VLSI, 1993, pp. 105-106.
11. H. J. Prömel and A. Steger, "RNC-approximation algorithms for the Steiner problem," in Proc. Symp. Theor. Aspect. Comput. Sci., Lecture Notes in Computer Science, vol. 1200, R. Reischuk and M. Morvan, Eds., Berlin, Germany, Springer-Verlag, 1997, pp. 559-570.
12. Y. F. Wu, P. Widmayer, and C. K. Wong, "A faster approximation algorithm for the Steiner problem in graphs," Algorithmica, vol. 23, pp. 223-229, 1986.
13. A. Zelikovsky, "An 11/6-approximation algorithm for the network Steiner problem," Algorithmica. vol. 9, pp. 463-470, 1993.
14. F. K. Hwang, D. S. Richards, and P. Winter, The Steiner Tree Problem, Annals of Discrete Mathematics. Amsterdam, The Netherlands: North-Holland, 1992, vol. 53.
15. U. Fößmeier and M. Kaufmann, "Solving rectilinear Steiner tree problems exactly in theory and practice," in Proc. 5th Eur. Symp. Algorithms Lecture Notes in Computer Science, R. Burkard and G. Woeginger, Eds. Berlin, Germany: Springer-Verlag, 1997, vol. 1284, pp. 171-185.
16. J. L. Ganley and J. P. Cohoon, "Improved computation of optimal rectilinear Steiner minimal trees," Int. J. Comput. Geometry and Appl., vol. 7, pp. 457-472, 1997.
17. J. S. Salowe and D. M. Warme, "Thirty-five-point rectilinear Steiner minimal trees in a day," Networks, vol. 25, pp. 69-87, 1995.
18. D. M. Warme, P. Winter, and M. Zacharisen, "Exact algorithms for plane Steiner tree problems: A computational study," Dept. Comput. Sci., Univ. Copenhagen, Copenhagen, Denmark, Tech. Rep. DIKU-TR-98/11, 1998.
19. J. L. Ganley, "Computing optimal rectilinear Steiner trees: A survey and experimental evaluation," Discret. Appl. Math., vol. 90, pp. 161-171, 1999.
20. D. M. Warme, P. Winter, and M. Zacharisen, The GeoSteiner 3.0 package. [Online]. Available: ftp.diku.dk/diku/users/martinz/geosteiner-3.0.tar.gz.
21. G. Robins, Batched iterated 1-Steiner code. [Online]. Available: www.cs.virginia.edu/robins/steiner.tar.
22. S. Rajagopalan and V. V. Vazirani, "On the bidirected cut relaxation for the metric Steiner tree problem," in Proc. 10th ACM-SIAM Symp. Discr. Algorithms, 1999, pp. 742-751.
23. M. Hanan, "On Steiner's problem with rectilinear distance," SIAM J. Appl. Math., vol. 14, pp. 255-265, 1966.
24. G. Robins and J. S. Salowe, "Low-degree minimum spanning trees," Discret. Comput. Geometry, vol. 14, pp. 151-165, 1995.
25. J. Griffith, G. Robins, J. S. Salowe, and T. Zhang, "Closing the gap: Near-optimal Steiner trees in polynomial time," IEEE Trans. Computer-Aided Design, vol. 13, pp. 1351-1365, Nov. 1994.
26. M. Zachariasen, "Rectilinear full Steiner tree generation," Networks, vol. 33, pp. 125-143, 1999.
27. V. V. Vazirani, Approximation Algorithms. Berlin, Germany: Springer-Verlag, to be published, 2000.
28. G. Robins and A. Zelikovsky, "Improved Steiner tree approximation in graphs," in Proc. 11th ACM-SIAM Ann. Symp. Discret. Algorithms, 2000, pp. 770-779.
29. T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms. Cambridge, MA: MIT Press, 1990.
30. R.-H. Güting, O. Nurmi, and T. Ottmann, "Fast algorithms for direct enclosures and direct dominances," J. Algorithms, vol. 10, pp. 170-186, 1989.
31. M. Hollander and D. A. Wolfe, Nonparametric Statistical Methods, 2nd ed. New York: Wiley, 1999.