欧几里德Steiner树问题介绍及一种特殊情况的讨论The Introduction of Euclid Steiner Tree Problem and the Discussion of a Special Case

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The paper is a brief introduction to the Euclid Steiner tree problem, including definition of Steiner problem, its property and complexity. In addition, it introduces the structures of Steiner trees of the graphs that have three vertices or four vertices. Especially, it discusses the structure of Steiner tree of a special case in the graph that has five vertices.

 [1] 越民义. 最小网络斯坦纳树问题[M]. 上海: 上海科学技术出版社, 2006. [2] 堵丁柱. 谈谈斯坦纳树[J]. 数学通报, 1995(1): 25-30. [3] 堵丁柱. 关于Steiner树的Gilbert-Pollak猜想的证明[J]. 中国科学院院刊, 1993: 243-244. [4] 越民义. 斯坦纳树问题及其推广[J]. 前沿, 2002(6): 3-6. [5] Hwang, F.K. and Richard, D.S. (1992) Stenier Tree Problems. Networks, 22, 55-89. http://dx.doi.org/10.1002/net.3230220105 [6] 王家桢, 马良, 张慧珍. 欧式Steiner最小树的Delaunay三角网混合智能求解方法[J]. 上海理工大学学报, 2014(4): 351-352. [7] Cheng, X. and Du, D.Z. (2001) Steiner Trees in Industry, Volume 11 of Combinatorial Optimization. [8] Hwang, F.K., Richards, D.S. and Winter, P. (1992) The Steiner Tree Problem. Elsevier. [9] Gusfield, D. (1997) Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511574931 [10] 刘振宏, 马仲蕃. 关于Steiner最小树问题[J]. 运筹学学报, 1991(2). [11] Garey, M.R., Graham, R.L. and Johnson, D.S. (1977) The Complexity of Computing Steiner Minimal Trees. SIAM Journal on Applied Mathematics, 32, 835-859. http://dx.doi.org/10.1137/0132072 [12] 王付明. 四点集上的Steiner最小树[J]. 运筹学的理论与应用, 1996: 182-186.