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923
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
On the Steiner ratio in 3space
 J. of Combinatorial Theory, A
, 1992
"... The "Steiner minimal tree" (SMT) of a point set P is the shortest network of "wires" which will suffice to "electrically" interconnect P . The "minimum spanning tree" (MST) is the shortest such network when only intersite line segments are permitted. The " ..."
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Cited by 8 (1 self)
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. The "Steiner ratio" ae(P ) of a point set P is the length of its SMT divided by the length of its MST. It is of interest to understand which point set (or point sets) in R d have minimal Steiner ratio. In this paper, we introduce a point set in R d which we call the "ddimensional sausage
Approximation Algorithms for Directed Steiner Problems
 Journal of Algorithms
, 1998
"... We give the first nontrivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work we ..."
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Cited by 178 (8 self)
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We give the first nontrivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work
A polylogarithmic approximation algorithm for the group Steiner tree problem
 Journal of Algorithms
, 2000
"... The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich a ..."
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Cited by 149 (9 self)
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The group Steiner tree problem is a generalization of the Steiner tree problem where we ae given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimumweight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich
Three disproofs of the GilbertPollak conjecture on Steiner ratio in three or more dimensions
, 1994
"... The GilbertPollak conjecture, posed in 1968, was the most important conjecture in the area of "Steiner trees." The "Steiner minimal tree" (SMT) of a point set P is the shortest network of "wires" which will suffice to electrically interconnect P . The "minimum sp ..."
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Cited by 2 (0 self)
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The GilbertPollak conjecture, posed in 1968, was the most important conjecture in the area of "Steiner trees." The "Steiner minimal tree" (SMT) of a point set P is the shortest network of "wires" which will suffice to electrically interconnect P . The "
The Steiner Ratio for ObstacleAvoiding Rectilinear Steiner Trees
"... We consider the problem of finding a shortest rectilinear Steiner tree for a given set of points in the plane in the presence of rectilinear obstacles that must be avoided. We extend the Steiner ratio to the obstacleavoiding case and show that it is equal to the Steiner ratio for the obstaclefree ..."
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We consider the problem of finding a shortest rectilinear Steiner tree for a given set of points in the plane in the presence of rectilinear obstacles that must be avoided. We extend the Steiner ratio to the obstacleavoiding case and show that it is equal to the Steiner ratio for the obstacle
Integrality ratio for group steiner trees and directed steiner trees
 In 14th Annual ACMSIAM Symposium on Discrete Algorithms
, 2003
"... The natural relaxation for the Group Steiner Tree problem, as well as for its generalization, the Directed Steiner Tree problem, is a flowbased linear programming relaxation. We prove new lower bounds on the integrality ratio of this relaxation. For the Group Steiner Tree problem, we show the integ ..."
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Cited by 29 (6 self)
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The natural relaxation for the Group Steiner Tree problem, as well as for its generalization, the Directed Steiner Tree problem, is a flowbased linear programming relaxation. We prove new lower bounds on the integrality ratio of this relaxation. For the Group Steiner Tree problem, we show
Tighter Bounds for Graph Steiner Tree Approximation
 SIAM Journal on Discrete Mathematics
, 2005
"... Abstract. The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialln 3 time heuristic that achieves a bestknown approximation ratio of 1 + ≈ 1.55 for general graphs 2 and best ..."
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Cited by 88 (7 self)
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Abstract. The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialln 3 time heuristic that achieves a bestknown approximation ratio of 1 + ≈ 1.55 for general graphs 2 and best
The kSteiner Ratio in the Rectilinear Plane
, 1998
"... A Steiner minimum tree Ž SMT. in the rectilinear plane is the shortest length tree interconnecting a set of points, called the regular points, possibly using additional vertices. A ksize Steiner minimum tree Ž kSMT. is one that can be split into components where all regular points are leaves and al ..."
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Cited by 3 (0 self)
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and all components have at most k leaves. The kSteiner ratio in the rectilinear plane, � k, is the infimum of the ratios SMT�kSMT over all finite sets of regular points. The kSteiner ratio is used to determine the performance ratio of several recent polynomialtime approximations for Steiner minimum
Results 1  10
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923