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101,073
On the Location of Steiner Points in UniformlyOriented Steiner Trees
, 2001
"... We give a fundamental result on the location of Steiner points for Steiner minimum trees in uniform orientation metrics. As a corollary we obtain a linear time algorithm for constructing a Steiner minimum tree for a given full topology when the number of uniform orientations is = 3m, m 1. ..."
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Cited by 1 (1 self)
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We give a fundamental result on the location of Steiner points for Steiner minimum trees in uniform orientation metrics. As a corollary we obtain a linear time algorithm for constructing a Steiner minimum tree for a given full topology when the number of uniform orientations is = 3m, m 1.
An Exact Algorithm for the UniformlyOriented Steiner Tree Problem
 In Proceedings of the 10th European Symposium on Algorithms, Lecture Notes in Computer Science
, 2002
"... An exact algorithm to solve the Steiner tree problem for uniform orientation metrics in the plane is presented. The algorithm is based on the twophase model, consisting of full Steiner tree (FST) generation and concatenation, which has proven to be very successful for the rectilinear and Euclid ..."
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Cited by 18 (7 self)
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An exact algorithm to solve the Steiner tree problem for uniform orientation metrics in the plane is presented. The algorithm is based on the twophase model, consisting of full Steiner tree (FST) generation and concatenation, which has proven to be very successful for the rectilinear
Canonical Forms and Algorithms for Steiner Trees in Uniform Orientation Metrics
 In preparation
, 2002
"... We present some fundamental structural properties for minimum length networks (known as Steiner minimum trees) interconnecting a given set of points in an environment in which edge segments are restricted to uniformly oriented directions. We show that the edge segments of any full component o ..."
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Cited by 11 (4 self)
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We present some fundamental structural properties for minimum length networks (known as Steiner minimum trees) interconnecting a given set of points in an environment in which edge segments are restricted to uniformly oriented directions. We show that the edge segments of any full component
The Steiner Tree Problem in Orientation Metrics
 J. Comp. Syst. Sci
, 1997
"... Given a set \Theta of ff i (i = 1; 2; : : : ; k) orientations (angles) in the plane, one can define a distance function which induces a metric in the plane, called the orientation metric [3]. In the special case where all the angles are equal, we call the metric a uniform orientation metric [2]. Spe ..."
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Cited by 3 (1 self)
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Given a set \Theta of ff i (i = 1; 2; : : : ; k) orientations (angles) in the plane, one can define a distance function which induces a metric in the plane, called the orientation metric [3]. In the special case where all the angles are equal, we call the metric a uniform orientation metric [2
Rotational Steiner Ratio Problem Under Uniform Orientation Metrics ⋆
"... Abstract. Let P be a set of n points in a metric space. A Steiner Minimal Tree (SMT) on P is a shortest network interconnecting P while a Minimum Spanning Tree (MST) is a shortest network interconnecting P with all edges between points of P. The Steiner ratio is the infimum over P of ratio of the le ..."
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of the length of SMT over that of MST. Steiner ratio problem is to determine the value of the ratio. In this paper we consider the Steiner ratio problem in uniform orientation metrics, which find important applications in VLSI design. Our study is based on the fact that lengths of MSTs and SMTs could be reduced
Eliminating Steiner Vertices in Graph Metrics
"... Given an edgeweighted undirected graph G and a subset of “required” vertices R ⊆ V (G), called the terminals, we want to find a minor G ′ with possibly different edgeweights, that retains distances between all terminalpairs exactly, and is as small as possible. We prove that every graph G with n ..."
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vertices and k terminals can be reduced (in this sense) to a minor G ′ with O(k 4) vertices and edges. We also give a lower bound of Ω(k2) on the number of vertices required. The O(k4) upper bound on the size of the minor is achieved using a specific construction for minors, which we call Oriented Minors
Algorithms for the Steiner Problem in Networks
, 2003
"... The Steiner problem in networks is the problem of connecting a set of required vertices in a weighted graph at minimum cost. It is a classical N Phard problem with many important applications. For this problem we develop, implement and test several new techniques. On the side of lower bounds, we pr ..."
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The Steiner problem in networks is the problem of connecting a set of required vertices in a weighted graph at minimum cost. It is a classical N Phard problem with many important applications. For this problem we develop, implement and test several new techniques. On the side of lower bounds, we
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 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
Results 1  10
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101,073