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On the Approximation of the Rectilinear Steiner Arborescence Problem in the Plane
, 2000
"... We give a polynomial time approximation scheme (PTAS) for the rectilinear Steiner arborescence problem in the plane. The result is obtained by modifying Arora's PTAS for Euclidean TSP. The previously best known result was a 2approximation algorithm. Keywords: Analysis of algorithms, subopt ..."
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Cited by 1 (0 self)
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We give a polynomial time approximation scheme (PTAS) for the rectilinear Steiner arborescence problem in the plane. The result is obtained by modifying Arora's PTAS for Euclidean TSP. The previously best known result was a 2approximation algorithm. Keywords: Analysis of algorithms
A Polynomial Time Approximation Scheme for the Symmetric Rectilinear Steiner Arborescence Problem
, 2002
"... The Symmetric Rectilinear Steiner Arborescence (SRStA) problem is defined as follows: given a set of terminals in the positive quadrant of the plane, connect them using horizontal and vertical lines such that each terminal can be reached from the origin via a ymonotone path and the total length o ..."
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Cited by 4 (2 self)
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The Symmetric Rectilinear Steiner Arborescence (SRStA) problem is defined as follows: given a set of terminals in the positive quadrant of the plane, connect them using horizontal and vertical lines such that each terminal can be reached from the origin via a ymonotone path and the total length
A Heuristic Algorithm for the Rectilinear Steiner Arborescence Problem
 Engineering Optimization
, 1994
"... In this paper the following problem is considered: given a root node R in a mesh and a set D of nodes from the mesh, construct a shortestpath tree rooted at R that spans the set D and minimizes the number of links used. The problem is equivalent as finding a Steiner tree in a directed mesh in whic ..."
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Cited by 6 (0 self)
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in which all the links point away from the root node R. The problem of finding a Steiner tree in such grid has been known in the literature as the Rectilinear Steiner Arborescence (RSA) problem. Rao et. al [9] have proposed an efficient heuristic algorithm for a special case of this problem, in which all
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
On the Construction of Optimal or NearOptimal Rectilinear Steiner Arborescence
, 1994
"... Given a set of nodes N lying on the first quadrant of the Euclidean Plane E 2 , the Rectilinear Minimum Steiner Arborescence (RMSA) problem is to find a shortestpath tree of the minimum length rooted at the origin, containing all nodes in N , and composed solely of horizontal and vertical arcs or ..."
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Given a set of nodes N lying on the first quadrant of the Euclidean Plane E 2 , the Rectilinear Minimum Steiner Arborescence (RMSA) problem is to find a shortestpath tree of the minimum length rooted at the origin, containing all nodes in N , and composed solely of horizontal and vertical arcs
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
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 177 (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
Rectilinear Full Steiner Tree Generation
 NETWORKS
, 1997
"... The fastest exact algorithm (in practice) for the rectilinear Steiner tree problem in the plane uses a twophase scheme: First a small but sufficient set of full Steiner trees (FSTs) is generated and then a Steiner minimum tree is constructed from this set by using simple backtrack search, dynamic p ..."
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Cited by 26 (5 self)
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The fastest exact algorithm (in practice) for the rectilinear Steiner tree problem in the plane uses a twophase scheme: First a small but sufficient set of full Steiner trees (FSTs) is generated and then a Steiner minimum tree is constructed from this set by using simple backtrack search, dynamic
Approaching the 5/4Approximation for Rectilinear Steiner Trees
, 1995
"... The rectilinear Steiner tree problem requires a shortest tree spanning a given vertex subset in the plane with rectilinear distance. It was proved that the output length of Zelikovsky's [25] and Berman/Ramaiyer [3] heuristics is at most 1.375 and 97 72 1:347 of the optimal length, respectivel ..."
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Cited by 15 (6 self)
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The rectilinear Steiner tree problem requires a shortest tree spanning a given vertex subset in the plane with rectilinear distance. It was proved that the output length of Zelikovsky's [25] and Berman/Ramaiyer [3] heuristics is at most 1.375 and 97 72 1:347 of the optimal length
Highly scalable algorithms for rectilinear and octilinear Steiner trees
 In Proc. Asian and South Pacific Design Automation Conf
, 2003
"... problem, which asks for a minimumlength interconnection of a given set of terminals in the rectilinear plane, is one of the fundamental problems in electronic design automation. Recently there has been renewed interest in this problem due to the need for highly scalable algorithms able to handle ne ..."
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Cited by 29 (3 self)
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problem, which asks for a minimumlength interconnection of a given set of terminals in the rectilinear plane, is one of the fundamental problems in electronic design automation. Recently there has been renewed interest in this problem due to the need for highly scalable algorithms able to handle
Results 1  10
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