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Hardness and approximation of octilinear Steiner trees
 IN PROCEEDINGS OF THE 16TH INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION (ISAAC 2005
, 2005
"... Given a point set K of terminals in the plane, the octilinear Steiner tree problem is to find a shortest tree that interconnects all terminals and edges run either in horizontal, vertical, or ±45 ◦ diagonal direction. This problem is fundamental for the novel octilinear routing paradigm in VLSI de ..."
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Cited by 2 (1 self)
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Given a point set K of terminals in the plane, the octilinear Steiner tree problem is to find a shortest tree that interconnects all terminals and edges run either in horizontal, vertical, or ±45 ◦ diagonal direction. This problem is fundamental for the novel octilinear routing paradigm in VLSI
The Prize Collecting Steiner Tree Problem
, 2000
"... This work is motivated by an application in local access network design that can be modeled using the NPhard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primaldual 2approximation algorithm devised for it by Goemans and Williamson. We develop seve ..."
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Cited by 103 (1 self)
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This work is motivated by an application in local access network design that can be modeled using the NPhard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primaldual 2approximation algorithm devised for it by Goemans and Williamson. We develop
A Catalog of Steiner Tree Formulations
, 1993
"... We present some existing and some new formulations for the Steiner tree and Steiner arborescence problems. We show the equivalence of many of these formulations. In particular, we establish the equivalence between the classical bidirected dicut relaxation and two vertex weighted undirected relaxatio ..."
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Cited by 36 (0 self)
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We present some existing and some new formulations for the Steiner tree and Steiner arborescence problems. We show the equivalence of many of these formulations. In particular, we establish the equivalence between the classical bidirected dicut relaxation and two vertex weighted undirected
Steiner Tree NPcompleteness Proof
, 2003
"... This document is an exercise for the Computational Complexity course taken at the University of Trento. We propose an NPcompleteness proof for the Steiner Tree problem in graphs. ..."
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Cited by 1 (0 self)
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This document is an exercise for the Computational Complexity course taken at the University of Trento. We propose an NPcompleteness proof for the Steiner Tree problem in graphs.
Models for the Steiner Tree Packing Problem
, 2013
"... The Steiner tree packing problem is a long studied problem in combinatorial optimization. In contrast to many other problems, where an enormous progress has been made in the practical problem solving, the Steiner tree packing problem remains very difficult. Most heuristics schemes are ineffective ..."
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The Steiner tree packing problem is a long studied problem in combinatorial optimization. In contrast to many other problems, where an enormous progress has been made in the practical problem solving, the Steiner tree packing problem remains very difficult. Most heuristics schemes are ineffec
Approximating the Weight of Shallow Steiner Trees
 DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science
, 1998
"... This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set of k vertices in a graph. Exact solutions or logarithmic ratio approximation algorithms were known before for the cases of d <= 5. Here we give a polynomial time appr ..."
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Cited by 32 (3 self)
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This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set of k vertices in a graph. Exact solutions or logarithmic ratio approximation algorithms were known before for the cases of d <= 5. Here we give a polynomial time
Packing Steiner trees: polyhedral investigations
, 1992
"... Let G = (V; E) be a graph and T ` V be a node set. We call an edge set S a Steiner tree with respect to T if S connects all pairs of nodes in T. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph G = (V; E) with edge weights w e, ed ..."
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Cited by 17 (5 self)
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Let G = (V; E) be a graph and T ` V be a node set. We call an edge set S a Steiner tree with respect to T if S connects all pairs of nodes in T. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph G = (V; E) with edge weights w e
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
Algorithms for Plane Steiner Tree Problems
, 1998
"... Topological network design is the process of planning the layout of a network subject to constraints on topology. Applications include the design of transportation and communication networks where the construction costs typically are associated with the nodes and/or edges of the network. The Steiner ..."
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Cited by 1 (0 self)
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. The Steiner tree problem is one of the fundamental topological network design problems. The problem is to interconnect (a subset of) the nodes such that there is a path between every pair of nodes while minimizing the total cost of selected edges. Originally, the Steiner tree problem was stated as a purely
NodeWeighted Steiner Tree and Group Steiner Tree in Planar Graphs
"... We improve the approximation ratios for two optimization problems in planar graphs. For nodeweighted Steiner tree, a classical networkoptimization problem, the best achievable approximation ratio in general graphs is Θ(log n), and nothing better was previously known for planar graphs. We give a c ..."
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Cited by 25 (2 self)
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We improve the approximation ratios for two optimization problems in planar graphs. For nodeweighted Steiner tree, a classical networkoptimization problem, the best achievable approximation ratio in general graphs is Θ(log n), and nothing better was previously known for planar graphs. We give a
Results 21  30
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