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

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

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.

Some Formulations for the Group Steiner Tree Problem

2004 ◽  
Vol 18 ◽  
pp. 127-132 ◽  
Author(s):  
Carlos E. Ferreira ◽  
Fernando M. de Oliveira Filho
Keyword(s):  
Steiner Tree ◽  
Steiner Tree Problem ◽  
Group Steiner Tree

scholarly journals Keyword-Based Knowledge Graph Exploration Based on Quadratic Group Steiner Trees

2021 ◽  
Author(s):  
Yuxuan Shi ◽  
Gong Cheng ◽  
Trung-Kien Tran ◽  
Jie Tang ◽  
Evgeny Kharlamov
Keyword(s):  
Steiner Tree ◽  
Exact Algorithm ◽  
Query Languages ◽  
Steiner Tree Problem ◽  
Underlying Structure ◽  
Graph Exploration ◽  
Group Steiner Tree ◽  
The Cost ◽  
Semantic Distances ◽  
Quadratic Group

Exploring complex structured knowledge graphs (KGs) is challenging for non-experts as it requires knowledge of query languages and the underlying structure of the KGs. Keyword-based exploration is a convenient paradigm, and computing a group Steiner tree (GST) as an answer is a popular implementation. Recent studies suggested improving the cohesiveness of an answer where entities have small semantic distances from each other. However, how to efficiently compute such an answer is open. In this paper, to model cohesiveness in a generalized way, the quadratic group Steiner tree problem (QGSTP) is formulated where the cost function extends GST with quadratic terms representing semantic distances. For QGSTP we design a branch-and-bound best-first (B3F) algorithm where we exploit combinatorial methods to estimate lower bounds for costs. This exact algorithm shows practical performance on medium-sized KGs.

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