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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.
Packing Steiner trees
"... The Steiner packing problem is to find the maximum number of edgedisjoint subgraphs of a given graph G that connect a given set of required points S. This problem is motivated by practical applications in VLSIlayout and broadcasting, as well as theoretical reasons. In this paper, we study this p ..."
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Cited by 108 (5 self)
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this problem and present an algorithm with an asymptotic approximation factor of S/4. This gives a sufficient condition for the existence of k edgedisjoint Steiner trees in a graph in terms of the edgeconnectivity of the graph. We will show that this condition is the best possible if the number
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
Improved Steiner Tree Approximation in Graphs
, 2000
"... The Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialtime heuristic with an approximation ratio approaching 1 + 2 1:55, which improves upon the previously bestknown approximation ..."
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Cited by 225 (6 self)
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The Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialtime heuristic with an approximation ratio approaching 1 + 2 1:55, which improves upon the previously best
Approximating Steiner trees
, 2006
"... We give a presentation of Robins and Zelikovsky’s 1.55 approximation algorithm to the Steiner Tree Problem and a thorough proof of its approximation ratio. Furthermore we sketch a proof by Thimm bounding the approximability of the Steiner Tree Problem. 1 ..."
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We give a presentation of Robins and Zelikovsky’s 1.55 approximation algorithm to the Steiner Tree Problem and a thorough proof of its approximation ratio. Furthermore we sketch a proof by Thimm bounding the approximability of the Steiner Tree Problem. 1
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 9 (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
Advances in Steiner Trees
 Advances in Steiner Trees
, 1998
"... We present a computational study of exact algorithms for the Euclidean and rectilinear Steiner tree problems in the plane. These algorithms  which are based on the generation and concatenation of full Steiner trees  are much more efficient than other approaches and allow exact solutions of pro ..."
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Cited by 1 (0 self)
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We present a computational study of exact algorithms for the Euclidean and rectilinear Steiner tree problems in the plane. These algorithms  which are based on the generation and concatenation of full Steiner trees  are much more efficient than other approaches and allow exact solutions
Minimum Moment Steiner Trees
"... For a rectilinear Steiner tree T with a root, define its . . . k du, where the integration is over all edges of T, dT (u) is the length of the unique path in T from the root to u, and du is the incremental edge length. Given a set of points P in the plane, a kth moment Steiner Minimum Tree (kSMT) ..."
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Cited by 2 (0 self)
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For a rectilinear Steiner tree T with a root, define its . . . k du, where the integration is over all edges of T, dT (u) is the length of the unique path in T from the root to u, and du is the incremental edge length. Given a set of points P in the plane, a kth moment Steiner Minimum Tree (k
PseudoGilbert–Steiner Trees
, 1994
"... Abstract: The Gilbert network problem is a generalization of the Steiner minimal tree problem derived by adding flowdependent weights to the edges. In this paper, we define a special class of minimum Gilbert networks, called pseudoGilbert–Steiner trees, and we show that it can be constructed by Gi ..."
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Abstract: The Gilbert network problem is a generalization of the Steiner minimal tree problem derived by adding flowdependent weights to the edges. In this paper, we define a special class of minimum Gilbert networks, called pseudoGilbert–Steiner trees, and we show that it can be constructed
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
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