scholarly journals Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs

2014 ◽  
Vol 10 (3) ◽  
pp. 1-20 ◽  
Author(s):  
Erik D. Demaine ◽  
Mohammadtaghi Hajiaghayi ◽  
Philip N. Klein
Keyword(s):  
Steiner Tree ◽  
Planar Graphs ◽  
Group Steiner Tree

scholarly journals Some formulations for the group steiner tree problem

2006 ◽  
Vol 154 (13) ◽  
pp. 1877-1884 ◽  
Author(s):  
Carlos E. Ferreira ◽  
Fernando M. de Oliveira Filho
Keyword(s):  
Steiner Tree ◽  
Steiner Tree Problem ◽  
Group Steiner Tree

New Reduction Techniques for the Group Steiner Tree Problem

2007 ◽  
Vol 17 (4) ◽  
pp. 1176-1188 ◽  
Author(s):  
Carlos Eduardo Ferreira ◽  
Fernando M. de Oliveira Filho
Keyword(s):  
Steiner Tree ◽  
Steiner Tree Problem ◽  
Reduction Techniques ◽  
Group Steiner Tree

Connected Set-Cover and Group Steiner Tree

2016 ◽  
pp. 430-432 ◽  
Author(s):  
Lidong Wu ◽  
Huijuan Wang ◽  
Weili Wu
Keyword(s):  
Steiner Tree ◽  
Set Cover ◽  
Connected Set ◽  
Group Steiner Tree ◽  
Connected Set Cover

MULTICASTING AND BROADCASTING IN UNDIRECTED WDM NETWORKS AND QoS EXTENTIONS OF MULTICASTING

2004 ◽  
Vol 15 (01) ◽  
pp. 187-203
Author(s):  
YINLONG XU ◽  
LI LIN ◽  
GUOLIANG CHEN ◽  
YINGYU WAN ◽  
WEIJUN GUO
Keyword(s):  
Steiner Tree ◽  
Constant Factor ◽  
Wdm Networks ◽  
Approximate Algorithm ◽  
Performance Ratio ◽  
Steiner Tree Problem ◽  
Log P ◽  
Auxiliary Graph ◽  
Group Steiner Tree ◽  
The Cost

This paper addresses multicasting and broadcasting in undirected WDM networks and QoS extensions of multicasting. It is given an undirected network G=(V, E), with Λ is the set of the available wavelengths in G, and associated with each edge, there is a subset of wavelengths on it. For a multicast request r=(s, D) with a source s and a set D of destinations, it is to find a tree rooted at s including all nodes in D such that the cost of the tree is minimized in terms of the cost of wavelength conversion at nodes and the cost of using wavelength on edges. This paper proves that multicasting in this model of networks is NP-Hard and cannot be approximated within a constant factor, unless P=NP. Furthermore, an auxiliary graph is constructed for the original WDM network, the multicasting is reduced to a group Steiner tree problem on the auxiliary graph and an approximate algorithm based on the group Steiner tree algorithm proposed by M. Charikar et al. with performance ratio of O( log 2(nk) log log (nk) log p) is provided, where k=|Λ| and p=|D∪{s}|. At last, some QoS extensions of multicasting are discussed.

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