A New Geometric Algorithm for Steiner Minimal Tree Problem by referring Visualization Experiment

2009 ◽  
Author(s):  
ZongXiao Yang ◽  
JieYu Hao ◽  
YanPing Gao ◽  
Kun Ye
Keyword(s):  
Minimal Tree ◽  
Steiner Minimal Tree ◽  
Geometric Algorithm ◽  
Visualization Experiment

scholarly journals Geometry-Experiment Algorithm for Steiner Minimal Tree Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zong-Xiao Yang ◽  
Xiao-Yao Jia ◽  
Jie-Yu Hao ◽  
Yan-Ping Gao
Keyword(s):  
Shortest Path ◽  
Optimization Problems ◽  
Minimal Tree ◽  
Steiner Minimal Tree ◽  
Combinatorial Optimization Problems ◽  
Visualization Experiment ◽  
Steiner Minimum Tree ◽  
The Given ◽  
Basic Philosophy ◽  
Delaunay Diagram

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.

The Global Shortest Path Visualization Approach with Obstructions

2015 ◽  
Vol 27 (5) ◽  
pp. 579-585 ◽  
Author(s):  
Guan-Qiang Dong ◽  
◽  
Zong-Xiao Yang ◽  
Lei Song ◽  
Kun Ye ◽  
...  
Keyword(s):  
Shortest Path ◽  
Planning Problem ◽  
Minimal Tree ◽  
Steiner Minimal Tree ◽  
Visualization Experiment ◽  
Np Hard Problem ◽  
Experiment Device ◽  
Steiner Minimum Tree ◽  
To Receive ◽  
Path Planning Problem

<div class=""abs_img""> <img src=""[disp_template_path]/JRM/abst-image/00270005/15.jpg"" width=""200"" />Shortest path experiment device</div> The avoidance obstacle path planning problem is stated in an obstacle environment. The minimum Steiner tree theory is the basis of the global shortest path. It is one of the classic NP-hard problem in nonlinear combinatorial optimization. A visualization experiment approach has been used to find Steiner point and system’s shortest path is called Steiner minimum tree. However, obstacles must be considered in some problems. An Obstacle Avoiding Steiner Minimal Tree (OASMT) connects some points and avoids running through any obstacle when constructing a tree with a minimal total length. We used a geometry experiment approach (GEA) to solve OASMT by using the visualization experiment device discussed below. A GEA for some systems with obstacles is used to receive approximate optimizing results. We proved the validity of the GEA for the OASMT by solving problems in which the global shortest path is obtained successfully by using the GEA. </span>

ACO-Steiner: Ant Colony Optimization Based Rectilinear Steiner Minimal Tree Algorithm

2006 ◽  
Vol 21 (1) ◽  
pp. 147-152 ◽  
Author(s):  
Yu Hu ◽  
Tong Jing ◽  
Zhe Feng ◽  
Xian-Long Hong ◽  
Xiao-Dong Hu ◽  
...  
Keyword(s):  
Ant Colony Optimization ◽  
Ant Colony ◽  
Minimal Tree ◽  
Steiner Minimal Tree ◽  
Tree Algorithm

GENERALIZED MELZAK'S CONSTRUCTION IN THE STEINER TREE PROBLEM

2002 ◽  
Vol 12 (06) ◽  
pp. 481-488 ◽  
Author(s):  
JIA F. WENG
Keyword(s):  
Steiner Tree ◽  
Euclidean Plane ◽  
Steiner Tree Problem ◽  
Minimal Tree ◽  
Steiner Minimal Tree ◽  
The Core ◽  
Steiner Minimal Trees ◽  
Minimum Networks ◽  
Set Of Points ◽  
The Given

For a given set of points in the Euclidean plane, a minimum network (a Steiner minimal tree) can be constructed using a geometric method, called Melzak's construction. The core of the Melzak construction is to replace a pair of terminals adjacent to the same Steiner point with a new terminal. In this paper we prove that the Melzak construction can be generalized to constructing Steiner minimal trees for circles so that either the given points (terminals) are constrained on the circles or the terminal edges are tangent to the circles. Then we show that the generalized Melzak construction can be used to find minimum networks separating and surrounding circular objects or to find minimum networks connecting convex and smoothly bounded objects and avoiding convex and smoothly bounded obstacles.

A neural network for the Steiner minimal tree problem

1994 ◽  
Vol 70 (5) ◽  
pp. 485-494 ◽  
Author(s):  
Jayadeva ◽  
Basabi Bhaumik
Keyword(s):  
Neural Network ◽  
Minimal Tree ◽  
Steiner Minimal Tree
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