The class Steiner minimal tree problem: A lower bound and test problem generation

Acta Informatica

Volumn 37, Issue 3, 2000, Pages 193-211

  Yang, Boting ^a   Gillard, Paul ^a  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034310322     PISSN: 00015903     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002360000042     Document Type: Article

References (37)

1. 1. M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming: Theory and Algorithms, New York: Wiley 1993
2. 2. J.E. Beasley, An algorithm for the Steiner problem in graphs, Networks 14, 147-159 (1984)
3. 3. J.E. Beasley, An SST-based algorithm for the Steiner problem in graphs, Networks 19, 1-16 (1989)
4. 4. K. Bharath-Kumar, J.M. Jaffe, Routing to multiple destinations in computer networks, IEEE Trans Commun 31, 343-351 (1983)
5. 5. G. Corneujols, M.L. Fisher, G.L. Nemhauser, Location of bank accounts to optimize float, Management Science 23, 789-810 (1977)
6. 6. D. Erlenkotter, A dual based procedure for uncapacitated facility location, Oper Res 26, 992-1009 (1978)
7. 7. M.L. Fisher, The Lagrangean relaxation method for solving integer programming problems. Management Science 27, 1-18 (1981)
8. 8. R.W. Floyd, Algorithm 97: Shortest paths, Communications of the ACM, Vol. 5, 345, 1962
9. 9. L.R. Foulds, V.J. Rayward-Smith, Steiner problems in graphs: algorithms and applications. Engineering Optimization 7, 7-16 (1983)
10. 10. B. Gavish, Topological design of centralized computer networks - formulations and algorithms, Networks 12, 355-377 (1982)
11. 11. A.M. Geoffrion, Lagrangean relaxation and its uses in integer programming, Mathematical Programming Study 2, 82-114 (1974)
12. 12. A.M. Geoffrion, G.W. Graves, Multicommodity distribution system design by Benders decomposition, Management Science 20, 822-844 (1974)
13. 13. M. Hanan, Layout, interconnection and placement, Networks 5, 85-88 (1975)
14. 14. M. Held, R.M. Karp, The traveling salesman problem and minimum spanning trees, Oper Res 18, 1138-1162 (1970)
15. 15. E. Ihler, Bounds on the quality of approximate solutions to the group Steiner problem, 16th International Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science 484, 109-118 (1990)
16. 16. E. Ihler, G. Reich, P. Widmayer, Class Steiner trees and VLSI-design, Discrete App Math 15, 173-194 (1999)
17. 17. R.M. Karp, Reducibility among combinatorial problems, In: Complexity of Computer Computations, R.E. Miller, J.W. Thatcher (Eds.), pp. 85-103, New York: Plenum Press, 1972
18. 18. B.N. Khoury, P.M. Pardalos, D.-Z. Du, A test problem generator for the Steiner problem in graphs, ACM Trans Math Softw 19, 509-522 (1993)
19. 19. B.N. Khoury, P.M. Pardalos, An exact branch and bound algorithm for the Steiner problem in graphs, First International Computing and Combinatorics Conference, Lecture Notes in Computer Science, Vol. 959, pp. 582-590 Berlin Heidelberg New York: Springer 1995
20. 20. B.N. Khoury, P.M. Pardalos, A heuristic for the Steiner problem on graphs, Comput Opt Appl 6, 5-14 (1996)
21. 21. V.P. Kompella, J.C. Pasquale, G.C. Polyzos, Multicast Routing for Multimedia Communication, IEEE/ACM Transactions on Networking 1, 286-292 (1993)
22. 22. L. Kou, G. Markowsky, L. Berman, A fast algorithm for Steiner trees, Acta Informatica 15, 141-145 (1981)
23. 23. E.L. Lawler, Combinatorial Optimization:Networks and Matroids, New York: Holt, Rinehart and Winston, 1976
24. 24. T. Lengauer, Combinatorial Algorithms for Integrated Circuit Layout, New York: Wiley, 1990
25. 25. Y. Leung, B. Yang, Lower bound for multimedia multicast routing, IEE Proceeding: Communications 145, No.2, 87-90 (1998)
26. 26. X.L. Lin, L.M. Ni, Multicast communication in multicomputer networks, IEEE Trans Parallel Distrib Syst 4, 1105-1117 (1993)
27. 27. G.L. Nemhauser, L.A. Wolsey, Integer and Combinatorial Optimization, New York: Wiley 1988
28. 28. P.M. Pardalos, D.-Z. Du (Eds.), Network Design: Connectivity and Facilities Location, DIMACS Series, 40, American Mathematical Society, 1998
29. 29. R.C. Prim, Shortest connection networks and some generalizations, Bell System Technical Journal 36, 1389-1401 (1957)
30. 30. C.R. Reeves (Ed.), Modern Heuristic Techniques for Combinatorial Problems, London: Blackwell Scientific Publications, 1993
31. 31. G. Reich, P. Widmayer, Beyond Steiner's problem: a VLSI oriented generalization, 15th International Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 411, pp. 196-210, 1989
32. 32. J.S. Rose, D.R. Blythe, W.M. Snelgrove, Z.G. Vranesic, Fast, high, quality VLSI placement on an MIMD multiprocessor, Proceeding of the IEEE International Conference on Computer-Aided Design, IEEE, New York, pp. 42-45, 1986
33. 33. J.M. Smith, J.S. Liebman, Steiner trees, Steiner circuits, and the interference problem in building design, Engineering Optimization 4, 15-36 (1986)
34. 34. Y. Tanaka, P.C. Huang, Multiple destination routing algorithms, IEICE Trans Commun, E78-B, 544-552 (1993)
35. 35. D.C. Verma, P.M. Gopal, Routing reserved bandwidth multipoint Connections, Comput Commun Rev 23, 96-105 (1993)
36. 36. B.M. Waxman, Routing of multi-point Connections, IEEE Journal on Select Areas in Communications 6, 1617-1622, (1988)
37. 37. Y.F. Wu, P. Widmayer, C.K. Wong, A faster approximation algorithm for the Steiner problem in graphs, Acta Informatica 23, 223-229 (1986)