A heuristic algorithm for Euclidean Steiner Minimal Tree inside simple polygon

2012 ◽  
Author(s):  
Elham Pashaei ◽  
Ali Nourollah ◽  
Alireza Bagheri
Keyword(s):  
Heuristic Algorithm ◽  
Simple Polygon ◽  
Minimal Tree ◽  
Steiner Minimal Tree

AN 0 (N log N) HEURISTIC ALGORITHM FOR THE RECTILINEAR STEINER MINIMAL TREE PROBLEM

1980 ◽  
Vol 4 (4) ◽  
pp. 179-192 ◽  
Author(s):  
J. MACGREGOR SMITH ◽  
D. T. LEE ◽  
JUDITH S. LIEBMAN
Keyword(s):  
Heuristic Algorithm ◽  
Minimal Tree ◽  
Steiner Minimal Tree

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.

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