scholarly journals Approximating Steiner Trees and Forests with Minimum Number of Steiner Points

2015 ◽  
pp. 95-106
Author(s):  
Nachshon Cohen ◽  
Zeev Nutov
Keyword(s):  
Steiner Trees ◽  
Steiner Points ◽  
Minimum Number

scholarly journals Approximations for Steiner trees with minimum number of Steiner points

2001 ◽  
Vol 262 (1-2) ◽  
pp. 83-99 ◽  
Author(s):  
Donghui Chen ◽  
Ding-Zhu Du ◽  
Xiao-Dong Hu ◽  
Guo-Hui Lin ◽  
Lusheng Wang ◽  
...  
Keyword(s):  
Steiner Trees ◽  
Steiner Points ◽  
Minimum Number

scholarly journals On compatible triangulations with a minimum number of Steiner points

2020 ◽  
Vol 835 ◽  
pp. 97-107
Author(s):  
Anna Lubiw ◽  
Debajyoti Mondal
Keyword(s):  
Steiner Points ◽  
Minimum Number

scholarly journals Time delayed discounted Steiner trees to locate two or more discounted Steiner points

2016 ◽  
Vol 57 ◽  
pp. 253
Author(s):  
Kashyapa Sirinanda ◽  
Marcus Brazil ◽  
Peter Grossman ◽  
Hyam Rubinstein ◽  
Doreen Thomas
Keyword(s):  
Steiner Trees ◽  
Steiner Points

Reorganizing topologies of Steiner trees to accelerate their eliminations

2019 ◽  
Vol 12 (01) ◽  
pp. 2050003
Author(s):  
Aymeric Grodet ◽  
Takuya Tsuchiya
Keyword(s):  
Lower Bound ◽  
Higher Dimensions ◽  
Exact Algorithms ◽  
Steiner Trees ◽  
Steiner Tree Problem ◽  
Original Algorithm ◽  
Steiner Points ◽  
Euclidean Steiner Tree Problem ◽  
Correct Topology ◽  
Enumeration Scheme

We describe a technique to reorganize topologies of Steiner trees by exchanging neighbors of adjacent Steiner points. We explain how to use the systematic way of building trees, and therefore topologies, to find the correct topology after nodes have been exchanged. Topology reorganizations can be inserted into the enumeration scheme commonly used by exact algorithms for the Euclidean Steiner tree problem in [Formula: see text]-space, providing a method of improvement different than the usual approaches. As an example, we show how topology reorganizations can be used to dynamically change the exploration of the usual branch-and-bound tree when two Steiner points collide during the optimization process. We also turn our attention to the erroneous use of a pre-optimization lower bound in the original algorithm and give an example to confirm its usage is incorrect. In order to provide numerical results on correct solutions, we use planar equilateral points to quickly compute this lower bound, even in dimensions higher than two. Finally, we describe planar twin trees, identical trees yielded by different topologies, whose generalization to higher dimensions could open a new way of building Steiner trees.

On the location of Steiner points in uniformly-oriented Steiner trees

2002 ◽  
Vol 83 (5) ◽  
pp. 237-241 ◽  
Author(s):  
Benny K. Nielsen ◽  
Pawel Winter ◽  
Martin Zachariasen
Keyword(s):  
Steiner Trees ◽  
Steiner Points

scholarly journals Approximating survivable networks with minimum number of steiner points

Networks ◽  
2012 ◽  
Vol 60 (4) ◽  
pp. 245-252 ◽  
Author(s):  
Lior Kamma ◽  
Zeev Nutov
Keyword(s):  
Survivable Networks ◽  
Steiner Points ◽  
Minimum Number
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