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Journal of Applied Mathematics
Volume 2013, Article ID 367107, 10 pages
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.


It is well known that the Steiner minimal tree problem is one of the classical nonlinear combinatorial optimization problems. A visualization experiment approach succeeds in generating Steiner points automatically and showing the system shortest path, named Steiner minimum tree, physically and intuitively. However, it is difficult to form stabilized system shortest path when the number of given points is increased and irregularly distributed. Two algorithms, geometry algorithm and geometry-experiment algorithm (GEA), are constructed to solve system shortest path using the property of Delaunay diagram and basic philosophy of Geo-Steiner algorithm and matching up with the visualization experiment approach (VEA) when the given points increase. The approximate optimizing results are received by GEA and VEA for two examples. The validity of GEA was proved by solving practical problems in engineering, experiment, and comparative analysis. And the global shortest path can be obtained by GEA successfully with several actual calculations.