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Bounds on the Maximum Number of Edgedisjoint Steiner Trees of a Graph
 Congressus Numerantium
, 2000
"... Tutte and NashWilliams, independently, gave necessary and sufficient conditions for a connected graph to have at least t edgedisjoint spanning trees. Gusfield introduced the concept of edgetoughness (G) of a connected graph G, defined as the minimum jSj=(!(G S) 1) taken over all edgedisconnectin ..."
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Cited by 4 (0 self)
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connectivity (G) has at least b (G)=2c edgedisjoint spanning trees. In this paper we investigate to which extent the above results can be generalized to a graph G = (V; E) with a distinguished subset of vertices K. We obtain lower bounds for the maximum number of edgedisjoint Steiner trees of G (minimal trees
Hardness and Approximation Results for Packing Steiner Trees
 LECTURE NOTES IN COMPUTER SCIENCE
, 2004
"... We study approximation algorithms and hardness of approximation for several versions of the problem of packing Steiner trees. For packing edgedisjoint Steiner trees of undirected graphs, we show APXhardness for 4 terminals. For packing Steinernodedisjoint Steiner trees of undirected graphs, we ..."
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Cited by 17 (1 self)
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We study approximation algorithms and hardness of approximation for several versions of the problem of packing Steiner trees. For packing edgedisjoint Steiner trees of undirected graphs, we show APXhardness for 4 terminals. For packing Steinernodedisjoint Steiner trees of undirected graphs, we
Packing Steiner trees
"... The Steiner packing problem is to find the maximum number of edgedisjoint subgraphs of a given graph G that connect a given set of required points S. This problem is motivated by practical applications in VLSIlayout and broadcasting, as well as theoretical reasons. In this paper, we study this p ..."
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Cited by 108 (5 self)
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this problem and present an algorithm with an asymptotic approximation factor of S/4. This gives a sufficient condition for the existence of k edgedisjoint Steiner trees in a graph in terms of the edgeconnectivity of the graph. We will show that this condition is the best possible if the number
Hardness and Approximation Results for . . .
"... We study approximation algorithms and hardness of approximation for several versions of the problem of packing Steiner trees. For packing edgedisjoint Steiner trees of undirected graphs, we show APXhardness for 4 terminals. For packing Steinernodedisjoint Steiner trees of undirected graphs, we sh ..."
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We study approximation algorithms and hardness of approximation for several versions of the problem of packing Steiner trees. For packing edgedisjoint Steiner trees of undirected graphs, we show APXhardness for 4 terminals. For packing Steinernodedisjoint Steiner trees of undirected graphs, we
Approximation Algorithms and Hardness Results for Packing ElementDisjoint Steiner Trees
, 2008
"... We study the problem of packing elementdisjoint Steiner trees in graphs. We are given a graph and a designated subset of terminal nodes, and the goal is to find a maximum cardinality set of elementdisjoint trees such that each tree contains every terminal node. An element means a nonterminal node ..."
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Cited by 2 (0 self)
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elementdisjoint Steiner trees in a planar graph is NPhard. Similarly, the problem of finding two edgedisjoint Steiner trees in a planar graph is NPhard. We design an algorithm for planar graphs that achieves an approximation guarantee close to 2. In fact, given a planar graph that is k
On approximate minmax theorems of graph connectivity problems
, 2006
"... Given an undirected graph G and a subset of vertices S ` V (G), we call the vertices in S the terminal vertices and the vertices in V (G) S the Steiner vertices. In this thesis, we study two problems whose goals are to achieve high "connectivity " among the terminal vertices. The ..."
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Cited by 3 (0 self)
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. The first problem is the Steiner Tree Packing problem, where a Steiner tree is a tree that connects the terminal vertices (Steiner vertices are optional). The goal of this problem is to find a largest collection of edgedisjoint Steiner trees. The second problem is the Steiner RootedOrientation problem
Datacast: A Scalable and Efficient Reliable Group Data Delivery Service for Data Centers
"... Reliable Group Data Delivery (RGDD) is a pervasive traffic pattern in data centers. In an RGDD group, a sender needs to reliably deliver a copy of data to all the receivers. Existing solutions either do not scale due to the large number of RGDD groups (e.g., IP multicast) or cannot efficiently use ..."
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Cited by 2 (0 self)
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network bandwidth (e.g., endhost overlays). Motivated by recent advances on data center network topology designs (multiple edgedisjoint Steiner trees for RGDD) and innovations on network devices (practical innetwork packet caching), we propose Datacast for RGDD. Datacast explores two design spaces: 1
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige, Goldwasser, Lovász, Safra and Szegedy [42], and Arora and Safra [6] and shows that there exists a positive ɛ such that approximating
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 414 (21 self)
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problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most
Results 1  10
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1,554