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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 edge-disjoint subgraphs of a given graph G that connect a given set of required points S. This problem is motivated by practical applications in VLSI-layout 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 edge-disjoint Steiner trees in a graph in terms of the edge-connectivity of the graph. We will show that this condition is the best possible if the number
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 polynomial-time heuristic with an approximation ratio approaching 1 + 2 1:55, which improves upon the previously best-known 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 polynomial-time heuristic with an approximation ratio approaching 1 + 2 1:55, which improves upon the previously best
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 real-world 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 real-world structures like highways and oil
On the terminal Steiner tree problem
, 2002
"... We investigate a practical variant of the well-known 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 well-known 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
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
The full Steiner tree problem
, 2003
"... Motivated by the reconstruction of phylogenetic tree in biology, we study the full Steiner tree problem in this paper. Given a complete graph G = (V; E) with a length function on E and a proper subset R ⊂ V, the problem is to 4nd a full Steiner tree of minimum length in G, which is a kind of Steiner ..."
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Cited by 9 (1 self)
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Motivated by the reconstruction of phylogenetic tree in biology, we study the full Steiner tree problem in this paper. Given a complete graph G = (V; E) with a length function on E and a proper subset R ⊂ V, the problem is to 4nd a full Steiner tree of minimum length in G, which is a kind
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 k-th moment Steiner Minimum Tree (k-SMT) ..."
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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 k-th moment Steiner Minimum Tree (k
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
Pseudo-Gilbert–Steiner Trees
, 1999
"... The Gilbert network problem is a generalization of the Steiner minimal tree problem derived by adding flow-dependent weights to the edges. In this paper, we define a special class of minimum Gilbert networks, called pseudo-Gilbert–Steiner trees, and we show that it can be constructed by Gilbert’s g ..."
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The Gilbert network problem is a generalization of the Steiner minimal tree problem derived by adding flow-dependent weights to the edges. In this paper, we define a special class of minimum Gilbert networks, called pseudo-Gilbert–Steiner trees, and we show that it can be constructed by Gilbert’s
Results 1 - 10
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1,258