Paper:

# The Global Shortest Path Visualization Approach with Obstructions

## Guan-Qiang Dong, Zong-Xiao Yang, Lei Song, Kun Ye, and Gen-Sheng Li

Institute of Systems Science and Engineering, Henan Engineering Laboratory of Wind Power Systems,

Henan University of Science and Technology

Luoyang 471003, China

Shortest path experiment device

*J. Robot. Mechatron.*, Vol.27 No.5, pp. 579-585, 2015.

- [1] F. K. Hwang, D. S. Richards, and P. Winter, “The Steiner tree problem,” Annals of Discrete Mathematics, Vol.53, Elsevier Science Publishers, 1992.
- [2] X. Y. Li, G. Calinescu, and P. J. Wan, “Distributed construction of a planar spanner and routing for ad hoc wireless networks,” The 21
^{st}Annual Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM), 2002. - [3] C. Sertac and C. F. Bazlamaçcci, “A distributed heuristic algorithm for the rectilinear steiner minimal tree problem,” Institute of Electrical and Electronics Engineers Inc Vol.27, pp. 2083-2087, 2008.
- [4] M. Fampa and N. Maculan, “Using a conic formulation for finding Steiner minimal trees,” Kluwer Academic Publishers, 2004.
- [5] M. Karpinski and A. Zelikovsky, “New Approximation Algorithms for the Steiner Tree Problems,” J. of Combinatorial Optimization, Vol.1, pp. 47-65, 1997.
- [6] D. M. Warme, P. Winter, and M. Zachariasen, “Exact Algorithms for Plane Steiner Tree Problems: A Computational Study,” Technical Report DIKU-TR-98/11, 1998.
- [7] L. Luc, V. Sacha, and Z. Nicolasdesign, “An ant algorithm for the steiner tree problem in graphs,” EvoWorkshops 2007: EvoCOMNET, EvoFIN, EvoIASP, EvoINTERACTION, EvoMUSART, EvoSTOC and EvoTRANSLOG, pp. 42-51, 2007.
- [8] E. N. Gilbert and H. O. Pollak, “Steiner minimal trees,” SIAM J. Appl. Math., Vol.16, pp. 323-345, 1968.
- [9] Z. M. Fu and Z. P. Chen, “Beauty of bubble,” Science Development Monthly, Vol.29, No.11, pp. 788-796, 1990 (in Chinese).
- [10] Z. Shen, C. Chu, and Y. Li, “Efficient rectilinear Steiner tree construction with rectilinear blockages,” Proc. ICCD, pp. 38-44, 2005.
- [11] Z. X. Yang, Y. P. Gao, C. Y. Cheng et al., “A visualization approach for the Steiner minimal tree problem,” Systems engineering theory and practice, Vol.28, No.7, pp. 173-178, 2008 (in Chinese).
- [12] Z. X. Yang, “Visualization device of system shortest path programming,” Chinese Patent: ZL2006201301488, 2007.
- [13] Z. X. Yang, X. Y. Jia, J. Y. Hao, and Y. P. Gao, “Geometry-experiment algorithm for Steiner minimal tree problem,” J. of Applied Mathematics, Article ID 367107, 2013.
- [14] Y. P. Gao, B. B. Yang, Z. X. Yang et al., “Visualization Experimental Approaches for Power Grid Planning,” Power System Technology, Vol.33, No.2, pp. 51-55, 2009 (in Chinese).
- [15] Z. Feng, Y. Hu, T. Jing, X. Hong, X. Hu, and G. Yan, “An
*O(nlogn)*algorithm for obstacle-avoiding routing tree construction in the lambda-geometry plane,” Proc. ISPD, pp. 48-55, 2006. - [16] Y. Hu, Z. Feng, T. Jing, X. Hong, Y. Yang, G. Yu, X. Hu, and G. Yan, “FORst: a 3-step heuristic for obstacle-avoiding rectilinear Steiner minimal tree construction,” J. of Information and Computational Science, pp. 107-116, 2004.
- [17] Y. Shi, T. Jing, L. He, and Z. Feng, “CDCTree: novel obstacle-avoiding routing tree construction based on current driven circuit model,” Proc. ASP-DAC, pp. 630-635, 2006.
- [18] G. Eason, B. Noble, and I. N. Sneddon, “On certain integrals of Lipschitz-Hankel type involving products of Bessel functions,” Phil. Trans. Roy. Soc. London, Vol.A247, pp. 529-551, 1955.
- [19] J. C. Maxwell, “A Treatise on Electricity and Magnetism,” 3
^{rd}ed., Vol.2, pp. 68-73, Oxford: Clarendon, 1892. - [20] I. S. Jacobs and C. P. Bean, “Fine particles, thin films and exchange anisotropy,” Magnetism, Vol.3, pp. 271-350, New York: Academic, 1963.
- [21] 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.
- [22] 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.
- [23] Y. Yorozu, M. Hirano. K. Oka, and Y. Tagawa, “Electron spectroscopy studies on magneto-optical media and plastic substrate interface,” IEEE Transl. J. Magn. Japan, Vol.2, pp. 740-741, 1987 (Digests 9
^{th}Annual Conf. Magnetics Japan, p. 301, 1982). - [24] M. Young, “The Technical Writer’s Handbook,” Mill Valley, CA: University Science, 1989.

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