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2 STEINER TREE PROBLEM

by Instructor Mohammad, T. Hajiaghayi, Scribe Vaibhav Singh , 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

by Kamal Jain, Mohammad R. Salavatipoury, et al.
"... 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 ..."
Abstract - Cited by 108 (5 self) - Add to MetaCart
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

by Gabriel Robins, Alexander Zelikovsky , 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 ..."
Abstract - Cited by 225 (6 self) - Add to MetaCart
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

by Michael Herring , 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 ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
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

by Guohui Lin , Guoliang Xue , 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 ..."
Abstract - Cited by 9 (0 self) - Add to MetaCart
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

by Anders Schack-nielsen, Christian Wulff-nilsen , 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

by Chin Lung Lu, Chuan Yi Tang, Richard Chia-tung Lee , 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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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

by W. Qiu, et al.
"... 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) ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
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

by D. M. Warme, P. Winter, M. Zachariasen - 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 ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
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

by D. Trietsch, J. F. Weng , 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 of 1,258