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Group Steiner Tree
, 2011
"... During this lecture we will present approximation algorithms for three network ..."
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During this lecture we will present approximation algorithms for three network
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
Rectilinear Group Steiner Trees and Applications in VLSI Design
, 2000
"... Given a set of disjoint groups of points in the plane, the rectilinear group Steiner tree problem is the problem of finding a shortest interconnection (under the rectilinear metric) which includes at least one point from each group. This is an important generalization of the wellknown rectiline ..."
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Cited by 1 (0 self)
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Given a set of disjoint groups of points in the plane, the rectilinear group Steiner tree problem is the problem of finding a shortest interconnection (under the rectilinear metric) which includes at least one point from each group. This is an important generalization of the well
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
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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address is group Steiner tree: given a graph with edge weights and a collection of groups (subsets of nodes), find a minimumweight connected subgraph that includes at least one node from each group. The best approximation ratio known in general graphs is O(log 3 n), or O(log 2 n) when the host graph is a
15854: Approximations Algorithms Lecturer: R. Ravi Topic: Randomized Rounding: Group Steiner Tree Date: 11/9/05
"... In this lecture, we show how to use the Randomized Rounding to devise a polylogarithmic approximation algorithm for the group Steiner tree problem. Given a weighted undirected graph with some subsets of vertices called groups, the group Steiner tree problem is defined as finding a ..."
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In this lecture, we show how to use the Randomized Rounding to devise a polylogarithmic approximation algorithm for the group Steiner tree problem. Given a weighted undirected graph with some subsets of vertices called groups, the group Steiner tree problem is defined as finding a
Advanced Approximation Algorithms (CMU 15854B, Spring 2008) Lecture 10: Group Steiner Tree problem
, 2008
"... We will be studying the Group Steiner tree problem in this lecture. Recall that the classical Steiner tree problem is the following. Given a weighted graph G = (V, E), a subset S ⊆ V of the vertices, and a root r ∈ V, we want to find a minimum weight tree which connects all the vertices in S to r. T ..."
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We will be studying the Group Steiner tree problem in this lecture. Recall that the classical Steiner tree problem is the following. Given a weighted graph G = (V, E), a subset S ⊆ V of the vertices, and a root r ∈ V, we want to find a minimum weight tree which connects all the vertices in S to r
Capacitated Network Design Problems: Hardness, Approximation Algorithms, and Connections to Group Steiner Tree
"... We design combinatorial approximation algorithms for the Capacitated Steiner Network (CapSN) problem and the Capacitated Multicommodity Flow (CapMCF) problem. These two problems entail satisfying connectivity requirements when edges have costs and hard capacities. In CapSN, the flow has to be s ..."
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Cited by 2 (0 self)
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to be supported separately for each commodity while in CapMCF, the flow has to be sent simultaneously for all commodities. We show that the Group Steiner problem on trees ([12]) is a special case of both problems. This implies the first polylogarithmic lower bound for these problems by [17]. We then give various
Results 1  10
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