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2 STEINER TREE PROBLEM
, 2011
"... We study the Primal Dual approach in approximation algorithms for the NP hard problems of: Steiner tree problem andPrize collecting steiner tree problem. ..."
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We study the Primal Dual approach in approximation algorithms for the NP hard problems of: Steiner tree problem andPrize collecting steiner tree problem.
The Euclidean Steiner Tree Problem
, 2004
"... The Euclidean Steiner tree problem is solved by finding the tree with minimal Euclidean length spanning a set of fixed vertices in the plane, while allowing for the addition of auxiliary vertices (Steiner vertices). Steiner trees are widely used to design realworld structures like highways and oil ..."
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Cited by 1 (0 self)
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The Euclidean Steiner tree problem is solved by finding the tree with minimal Euclidean length spanning a set of fixed vertices in the plane, while allowing for the addition of auxiliary vertices (Steiner vertices). Steiner trees are widely used to design realworld structures like highways and oil
On the terminal Steiner tree problem
, 2002
"... We investigate a practical variant of the wellknown graph Steiner tree problem. In this variant, every target vertex is required to be a leaf vertex in the solution Steiner tree. We present hardness results for this variant as well as a polynomial time approximation algorithm with performance ratio ..."
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Cited by 8 (0 self)
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We investigate a practical variant of the wellknown graph Steiner tree problem. In this variant, every target vertex is required to be a leaf vertex in the solution Steiner tree. We present hardness results for this variant as well as a polynomial time approximation algorithm with performance
Algorithms for Plane Steiner Tree Problems
, 1998
"... Topological network design is the process of planning the layout of a network subject to constraints on topology. Applications include the design of transportation and communication networks where the construction costs typically are associated with the nodes and/or edges of the network. The Steiner ..."
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Cited by 2 (0 self)
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. The Steiner tree problem is one of the fundamental topological network design problems. The problem is to interconnect (a subset of) the nodes such that there is a path between every pair of nodes while minimizing the total cost of selected edges. Originally, the Steiner tree problem was stated as a purely
The Prize Collecting Steiner Tree Problem
 In Proceedings of the 11th Annual ACMSIAM Symposium on Discrete Algorithms
, 1998
"... This work is motivated by an application in local access network design that can be modeled using the NPhard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primaldual 2approximation algorithm devised for it by Goemans and Williamson. We develop seve ..."
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Cited by 103 (1 self)
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This work is motivated by an application in local access network design that can be modeled using the NPhard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primaldual 2approximation algorithm devised for it by Goemans and Williamson. We develop
On the Hardness of Full Steiner Tree Problems
, 2014
"... Given a weighted graph G = (V,E) and a subset R of V, a Steiner tree in G is a tree which spans all vertices in R. The vertices in V \R are called Steiner vertices. A full Steiner tree is a Steiner tree in which each vertex of R is a leaf. The full Steiner tree problem is to find a full Steiner tree ..."
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Given a weighted graph G = (V,E) and a subset R of V, a Steiner tree in G is a tree which spans all vertices in R. The vertices in V \R are called Steiner vertices. A full Steiner tree is a Steiner tree in which each vertex of R is a leaf. The full Steiner tree problem is to find a full Steiner
Steiner Tree Problems
, 2000
"... this article, we will review important developments in 1990s and discuss some open problems which may induce important developments in this centrary ..."
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Cited by 12 (3 self)
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this article, we will review important developments in 1990s and discuss some open problems which may induce important developments in this centrary
Probabilistic Models for the Steiner Tree Problem
"... We consider a probabilistic model for the Steiner Tree problem. Under this model the problem is defined in a 2stage setting over a firststage complete weighted graph having its vertices associated with a probability of presence (independently each from another) in the second stage. A firststage f ..."
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Cited by 6 (2 self)
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We consider a probabilistic model for the Steiner Tree problem. Under this model the problem is defined in a 2stage setting over a firststage complete weighted graph having its vertices associated with a probability of presence (independently each from another) in the second stage. A first
On approximation algorithms for the terminal Steiner tree problem
, 2004
"... The terminal Steiner tree problem is a special version of the Steiner tree problem, where a Steiner minimum tree has to be found in which all terminals are leaves. We prove that no polynomial time approximation algorithm for the terminal Steiner tree problem can achieve an approximation ratio less t ..."
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Cited by 11 (0 self)
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The terminal Steiner tree problem is a special version of the Steiner tree problem, where a Steiner minimum tree has to be found in which all terminals are leaves. We prove that no polynomial time approximation algorithm for the terminal Steiner tree problem can achieve an approximation ratio less
Two Heuristics for the Steiner Tree Problem
 JOURNAL OF GLOBAL OPTIMIZATION
, 1996
"... The Steiner tree problem is to find the tree with minimal Euclidean length spanning a set of fixed points in the plane, given the ability to add points (Steiner points). The problem is NPhard, so polynomialtime heuristics are desired. We present two such heuristics, both of which utilize an ef ..."
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Cited by 3 (0 self)
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The Steiner tree problem is to find the tree with minimal Euclidean length spanning a set of fixed points in the plane, given the ability to add points (Steiner points). The problem is NPhard, so polynomialtime heuristics are desired. We present two such heuristics, both of which utilize
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