Approximation algorithm for bottleneck Steiner tree problem in the Euclidean plane

2004 ◽  
Vol 19 (6) ◽  
pp. 791-794 ◽  
Author(s):  
Zi-Mao Li ◽  
Da-Ming Zhu ◽  
Shao-Han Ma
Keyword(s):  
Approximation Algorithm ◽  
Steiner Tree ◽  
Euclidean Plane ◽  
Steiner Tree Problem ◽  
Bottleneck Steiner Tree

Exact Algorithms for the Bottleneck Steiner Tree Problem

2009 ◽  
pp. 24-33 ◽  
Author(s):  
Sang Won Bae ◽  
Sunghee Choi ◽  
Chunseok Lee ◽  
Shin-ichi Tanigawa
Keyword(s):  
Steiner Tree ◽  
Exact Algorithms ◽  
Steiner Tree Problem ◽  
Bottleneck Steiner Tree

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.

scholarly journals A flow-dependent quadratic steiner tree problem in the Euclidean plane

Networks ◽  
2014 ◽  
Vol 64 (1) ◽  
pp. 18-28 ◽  
Author(s):  
Marcus N. Brazil ◽  
Charl J. Ras ◽  
Doreen A. Thomas
Keyword(s):  
Steiner Tree ◽  
Euclidean Plane ◽  
Steiner Tree Problem
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