The Steiner Tree Problem in Orientation Metrics

Journal of Computer and System Sciences

Volumn 55, Issue 3, 1997, Pages 529-546

  Yan, G Y ^a   Albrecht, A ^a,b   Young, G H F ^a   Wong, C K ^a,c  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b BerCom GmbH   (Germany)

^c IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; PROBLEM SOLVING; THEOREM PROVING;

ORIENTATION METRICS; STEINER TREE PROBLEM;

TREES (MATHEMATICS);

EID: 0031355185     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1997.1513     Document Type: Article

References (48)

1. M. Hanan, On Steiner's Problem with rectilinear distance, SIAM J. Appl. Math. 14 (1966), 255-265.
2. M. Sarrafzadeh and C. K. Wong, Hierarchical Steiner tree construction in uniform orientations, IEEE Trans. Computer-Aided Design 11 (1992), 1095-1203.
3. P. Widmayer, Y. F. Wu, and C. K. Wong, On some distance problems in fixed orientations, SIAM J. Computer 16 No. 48) (1987), 728-746.
4. D. T. Lee, C.-F. Shen, and C.-L. Ding, On Steiner tree problem with 45°routing, in "IEEE International Symposium on Circuits and Systems (ISCAS'95), May 1995," pp. 1680-1683.
5. D. T. Lee and C.-F. Shen, The Steiner minimal tree problem in the λ-geometry plane, in "7th International Symposium on Algorithms and Computations (ISAAC'96), Osaka, Japan, Dec. 1996," pp. 247-255.
6. L.-K. Hua, et al., Application of mathematical methods to wheat harvesting, Chinese Math. 2 (1962), 77-91.
7. R. L. France, A note on the optimum location of new machines in existing plant layouts, J. Indust. Engrg. 14 (1963), 57-59.
8. E. J. Cockayne, On the Steiner problem, Canad. Math. Bull. 10 (1967), 431-450.
9. R. Courant and H. Robbins, "What is Mathematics?," Oxford Univ. Press, New York, 1941.
10. E. N. Gilbert and H. O. Pollak, Steiner minimal trees, SIAM J. Appl. Math. 16 (1968), 1-29.
11. Z. A. Melzak, On the problem of Steiner, Canad. Math. Bull. 4 (1961), 143-148.
12. W. D. Smith, How to find Steiner minimal trees in Euclidean d-space?, Algorithmic 7 (1992), 137-177.
13. P. K. Agarwal and M. T. Shing, Algorithms for the special cases of rectilinear Steiner trees. I. Points on the boundary of a rectilinear rectangle, Networks 20 (1990), 453-485.
14. A. V. Aho, M. R. Garey, and F. K. Hwang, Rectilinear Steiner trees: Efficient special case algorithms, Networks 7 (1977), 37-58.
15. J. E. Beasley, A heuristic for Euclidean and rectilinear Steiner problem, Europ. J. Oper. Res. 58 (1992), 284-292.
16. M. W. Bern, Two probabilistic results on rectilinear Steiner trees, Algorithmica 3 (1988), 191-204.
17. T.-H. Chao and Y.-C. Hsu, Rectilinear Steiner tree constructions by local and global refinement, IEEE Trans. Computer Aided Design 13, No. 3 (1994), 303-309.
18. F. R. K. Chung and H. K. Hwang, The largest minimal rectilinear Steiner trees for a set of n points enclosed in a rectangle with given perimeter, Networks 9 (1979), 19-36.
19. J. P. Cohoon, D. S. Richards, and J. S. Schowe, An optimal Steiner tree algorithm for a net whose terminals lie on the perimeter of a rectangle, IEEE Trans. Computer Aided Design 9, No. 4 (1990), 398-407.
20. L. L. Deneen, G. M. Shute, and C. D. Thomborson, A probably fast, provably optimal algorithm for rectilinear Steiner trees, Random Structures and Algorithms 5, No. 4 (1994), 535-557.
21. A. M. Farley, S. T. Hedetniemi, and S. L. Mitchell, Rectilinear Steiner trees in rectangle trees, SIAM J. Algebra Discrete Methods 1 (1980), 70-81.
22. M. R. Garey and D. S. Johnson, The rectilinear Steiner tree problem is NP-complete, SIAM J. Appl. Math. 32 (1977), 826-834.
23. 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 13, No. 11 (1994), 1351-1365.
24. M. Hanan and J. M. Kurtzberg, Placement Techniques, in "Design Automation of Digital Systems," Vol. 1, "Theory and Techniques" (M. A. Breuer, Ed.), Chap. 5, pp. 213-282, Prentice-Hall, Englewood Cliffs, NJ, 1972.
25. J. M. Ho, G. Vijayan, and C. K. Wong, New algorithm for the rectilinear Steiner tree problem, IEEE Trans. Computer Aided Design 9, No. 2 (1990), 185-193.
26. F. K. Hwang, On Steiner minimal trees with rectilinear distance, SIAM J. Appl. Math. 30, No. 1 (1976), 104-114.
27. F. K. Hwang, The rectilinear Steiner problem, Design Automat. Fault Tolerant Comput. 3 (1978), 303-310.
28. F. K. Hwang, An O(nlog n) algorithm for suboptimal rectilinear Steiner trees, IEEE Trans. Circuits Systems CAS-26, No. 1 (1979), 75-77.
29. F. K. Hwang, An O(nlog n) algorithm for rectilinear minimal spanning trees, J. Assoc. Comput. Machin. 26 (1979), 177-182.
30. F. K. Hwang, D. S. Richards, and P. Winter, "The Steiner Tree Problem," North-Holland, New York, 1992.
31. F. K. Hwang and D. S. Richards, Steiner tree problems, Networks 22 (1992), 55-89.
32. A. B. Kahng and G. Robins, On performance bounds for a class of rectilinear Steiner tree heuristics in arbitrary dimension, IEEE Trans. Comput. Aided Design 11, No. 11 (1992), 1462-1465.
33. A. B. Kahng and G. Robins, A new class of iterative Steiner tree heuristic with good performance, IEEE Trans. Comput. Aided Design 11, No. 7, (1992), 893-902.
34. J. Komlos and M. T. Shing, Probabilistic partitioning algorithms for the rectilinear Steiner problem, Networks 15 (1985), 413-423.
35. J. H. Lee, N. K. Bose, and F. K. Hwang, Use of Steiner's problem in suboptimal routing in rectilinear metric, IEEE Trans. Circuits Systems CAS-23, No. 7 (1976), 470-476.
36. M. Pecht, "Placement and Routing of Electronic Modules," Dekker, New York, 1993.
37. D. Richards, Fast heuristic algorithms for rectilinear Steiner trees, Algorithmica 4 (1989), 191-207.
38. D. Richards and J. S. Salowe, Special convex cases for rectilinear Steiner minimal trees, in "Proc. NATO Workshop on Topological Network Design, 1989."
39. D. Richards and J. S. Salowe, A simple proof of Hwang's theorem for rectilinear Steiner minimal trees, Ann. Oper. Res. (1992).
40. D. Richards and J. S. Salowe, A linear-time algorithm to construct rectilinear Steiner minimal trees for k-extremal point sets, Algorithmica 7 (1992), 247-276.
41. M. Servit, Heuristic algorithms for rectilinear Steiner trees, Digit. Process 7 (1981), 21-32.
42. J. M. Smith, D. T. Lee, and J. S. Liebman, An O(N log N) heuristic algorithms for the rectilinear Steiner minimal tree problem, Eng. Optim. 4 (1980), 179-192.
43. T. Snyder, On minimal rectilinear Steiner trees in all dimensions, in "Proc. 6th Association on Computing Machinery, Symposium on Computational Geometry, 1990," pp. 311-320.
44. O(√n) time, in "Parallel Algorithms and Architectures," Lecture Notes in Computer Science, Vol. 269 (A. Albrecht, et al., Ed.), Springer-Verlag, Berlin, 1987, pp. 176-183.
45. V. A. Trubin, Subclass of the Steiner problem on a plane with rectilinear metric, Cybernetics 21 (1985), 320-324.
46. Y. T. Wong and M. Petch, A solution for Steiner's problem, in "Placement and Routing of Electronic Modules" (M. Petch, Ed.), Dekker, New York, 1993, pp. 261-304.
47. Y. Y. Yang and O. Wing, Suboptimal algorithm for a wire routing problem, IEEE Trans. Circuit Theory CT-19 (1972), 508-511.
48. Y. Y. Yang and O. Wing, On a multinet wiring problem, IEEE Trans. Circuit Theory CT-20 (1973), 250-252.