Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 367107, 10 pages
http://dx.doi.org/10.1155/2013/367107
Research Article

Geometry-Experiment Algorithm for Steiner Minimal Tree Problem

Institute of Systems Science and Engineering, Henan University of Science and Technology, Luoyang 471003, China

Received 13 November 2012; Revised 18 February 2013; Accepted 4 March 2013

Academic Editor: Yuri Sotskov

Copyright © 2013 Zong-Xiao Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. K Hwang, D. S Richards, and P Winter, The Steiner Tree Problem, vol. 53 of Annals of Discrete Mathematics, North-Holland, Amsterdam, The Netherlands, 1992. View at Zentralblatt MATH · View at MathSciNet
  2. X. Y Li, G Calinescu, and P. J Wan, “Distributed construction of a planar spanner and routing for ad hoc wireless networks,” in Proceedings of the 21st Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM '02), vol. 3, pp. 1268–1277, June 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. D Du and X Hu, Steiner Tree Problems in Computer Communication Networks, World Scientific Publishing, Singapore, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. F. K Hwang, D. S Richards, and P Winter, The Steiner Tree Problem, vol. 53 of Annals of Discrete Mathematics, North-Holland, Amsterdam, The Netherlands, 1992. View at Zentralblatt MATH · View at MathSciNet
  5. I. H.-R Jiang and Y. T Yu, “Configurable rectilinear steiner tree construction for SoC and nano technologies,” in Proceedings of the 26th IEEE International Conference on Computer Design (ICCD '08), pp. 34–39, Lake Tahoe, Calif, USA, October 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. L. Y Wu and J. H He, “The local tearing property of textiles with Steiner tree structure,” Advanced Materials Research, vol. 332–334, pp. 1429–1432, 2011. View at Publisher · View at Google Scholar
  7. L. Y Wu and J. H He, “Study on the stability of steiner tree structure of explosion-proof textiles,” Mathematical and Computational Applications, vol. 15, no. 5, pp. 936–939, 2010. View at Google Scholar · View at Scopus
  8. L. Y Wu and J. H He, “Explosion-proof textile with hierarchical Steiner tree structure,” Thermal Science, vol. 16, no. 2, pp. 343–344, 2012. View at Publisher · View at Google Scholar
  9. D. M Warme, P Winter, and M Zachariasen, “Exact algorithms for plane Steiner tree problems: a computational study,” Tech. Rep. DIKU-TR-98/11.1998-3, 1998. View at Google Scholar
  10. S. K Chang, “The generation of minimal trees with a Steiner topology,” Journal of the Association for Computing Machinery, vol. 19, pp. 699–711, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. E. A Thompson, “The method of minimum evolution,” Annals of Human Genetics, vol. 36, no. 3, pp. 333–340, 1973. View at Google Scholar · View at MathSciNet
  12. M Fampa and N Maculan, “Using a conic formulation for finding Steiner minimal trees,” Numerical Algorithms, vol. 35, no. 2-4, pp. 315–330, 2004. View at Google Scholar · View at Scopus
  13. M Karpinski and A Zelikovsky, “New approximation algorithms for the steiner tree problems,” Journal of Combinatorial Optimization, vol. 1, no. 1, pp. 47–65, 1997. View at Google Scholar · View at Scopus
  14. S Cinel and C. F Bazlamaçci, “A distributed heuristic algorithm for the rectilinear steiner minimal tree problem,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 27, no. 11, pp. 2083–2087, 2008. View at Publisher · View at Google Scholar
  15. L Luc, V Sacha, and Z Nicolasdesign, “An ant algorithm for the steiner tree problem in graphs,” in Proceedings of the EvoWorkshops, EvoCOMNET, EvoFIN, EvoIASP, EvoINTERACTION, EvoMUSART, EvoSTOC and EvoTRANSLOG, pp. 42–51, 2007. View at Publisher · View at Google Scholar
  16. T Koch and A Martin, “SteinLib Testdata Library,” 2002, http://elib.zib.de/steinlib/steinlib.php.
  17. B Toppur and J. M Smith, “A Sausage heuristic for Steiner minimal trees in three-dimensional euclidean space,” Journal of Mathematical Modelling and Algorithms, vol. 4, no. 2, pp. 199–217, 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. Z. M Fu and Z. P Chen, “Beauty of bubble,” Science Development Monthly, vol. 29, no. 11, pp. 788–796, 1990 (Chinese). View at Google Scholar
  19. Z. X Yang, Y. P Gao, C. Y Cheng, Z. Q Feng, and Z. J Zhang, “Visualization approach for the Steiner minimal tree problem,” System Engineering Theory and Practice, vol. 28, no. 7, pp. 173–178, 2008. View at Google Scholar · View at Scopus
  20. J. H. He and Y Liu, “Control of bubble size and bubble number in bubble electrospinning,” Computers & Mathematics with Applications, vol. 64, no. 5, pp. 1033–1035, 2012. View at Publisher · View at Google Scholar
  21. J. H. He, “Effect of temperature on surface tension of a bubble and hierarchical ruptured bubbles for nanofiber fabrication,” Thermal Science, vol. 16, no. 1, pp. 327–330, 2012. View at Google Scholar
  22. Z. X. Yang, “Visualization device of system shortest path programming,” Chinese Patent, ZL2006201301488, October 2007.
  23. E. N Gilbert and H. O Pollak, “Steiner minimal trees,” SIAM Journal on Applied Mathematics, vol. 16, pp. 323–345, 1968. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Y.-P Gao, B.-B Yang, Z.-X Yang, and J.-Y Hao, “Visualization experimental approaches for power grid planning,” Power System Technology, vol. 33, no. 2, pp. 51–55, 2009. View at Google Scholar
  25. X. Y Li, I Stojmenovic, and Y Wang, “Partial Delaunay triangulation and degree limited localized bluetooth scatternet formation,” IEEE Transactions on Parallel and Distributed Systems, vol. 15, no. 4, pp. 350–361, 2004. View at Publisher · View at Google Scholar · View at Scopus
  26. Z. A Melzak, “On the problem of Steiner,” Canadian Mathematical Bulletin, vol. 4, pp. 143–148, 1961. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet