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A 3/2Approximation Algorithm for the Multitwoedge Connected Subgraph Problem
, 2008
"... We present a 3approximation algorithm for the twoedge connected problem on a complete graph with nonnegative 2 costs, and multiedges allowed in the solution. Previously, 2 was the best known performance guarantee. ..."
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Cited by 1 (0 self)
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We present a 3approximation algorithm for the twoedge connected problem on a complete graph with nonnegative 2 costs, and multiedges allowed in the solution. Previously, 2 was the best known performance guarantee.
Depth first search and linear graph algorithms
 SIAM JOURNAL ON COMPUTING
, 1972
"... The value of depthfirst search or "backtracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components of an undirect ..."
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Cited by 1406 (19 self)
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The value of depthfirst search or "backtracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components
EdgeConnectivity Augmentation Preserving Simplicity
, 1997
"... Given a simple graph G = (V; E), the goal is to find a smallest set F of new edges such that G = (V; E [ F ) is kedgeconnected and simple. Very recently this problem was shown to be NPcomplete. In this paper we prove that if OPT k P is high enough  depending on k only  then OPT k S = OPT ..."
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Cited by 15 (8 self)
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Given a simple graph G = (V; E), the goal is to find a smallest set F of new edges such that G = (V; E [ F ) is kedgeconnected and simple. Very recently this problem was shown to be NPcomplete. In this paper we prove that if OPT k P is high enough  depending on k only  then OPT k S = OPT
Edgeconnectivity augmentation with partition constraints
 SIAM J. Discrete Mathematics
, 1999
"... When k is even the minmax formula for the partitionconstrained problem is a natural generalization of [3]. However this generalization fails when k is odd. We show that at most one more edge is needed when k is odd and we characterize the graphs that require such an extra edge. ..."
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Cited by 17 (10 self)
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When k is even the minmax formula for the partitionconstrained problem is a natural generalization of [3]. However this generalization fails when k is odd. We show that at most one more edge is needed when k is odd and we characterize the graphs that require such an extra edge.
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 502 (0 self)
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We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 475 (67 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
POLYNOMIAL TIME ALGORITHMS FOR EDGECONNECTIVITY AUGMENTATION PROBLEMS
, 2000
"... Given a graph G of n vertices and m edges, and a spanning subgraph H of G, the problem of finding a minimum weight set of edges of G, denoted as Aug 2 (H;G), to be added to H to make it 2edge connected, is known to be NPhard. We present polynomial time efficient algorithms for solving special case ..."
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Cited by 1 (1 self)
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Given a graph G of n vertices and m edges, and a spanning subgraph H of G, the problem of finding a minimum weight set of edges of G, denoted as Aug 2 (H;G), to be added to H to make it 2edge connected, is known to be NPhard. We present polynomial time efficient algorithms for solving special
Preserving And Increasing Local EdgeConnectivity In Mixed Graphs
 SIAM J. Discrete Math
, 1995
"... Generalizing and unifying earlier results of W. Mader and of the second and third authors, we prove two splitting theorems concerning mixed graphs. By invoking these theorems we obtain minmax formulae for the minimum number of new edges to be added to a mixed graph so that the resulting graph satis ..."
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Cited by 24 (7 self)
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for the corresponding optimization problems. 1. INTRODUCTION AND PRELIMINARIES Our main concern, the edgeconnectivity augmentation problem, is as follows. What is the minimum number (or, more generally, the minimum cost) fl of new edges to be added to M so that in the resulting graph M 0 the local edgeconnectivity
Augmenting EdgeConnectivity between Vertex Subsets
"... Given a graph G = (V, E) and a requirement function r: W1 × W2 → R+ for two families W1, W2 ⊆ 2V − {∅}, we consider the problem (called areatoarea edgeconnectivity augmentation problem) of augmenting G by a smallest number of new edges so that the resulting graph ˆ G satisfies δG ˆ(X) ≥ r(W1, W2) ..."
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Cited by 1 (0 self)
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Given a graph G = (V, E) and a requirement function r: W1 × W2 → R+ for two families W1, W2 ⊆ 2V − {∅}, we consider the problem (called areatoarea edgeconnectivity augmentation problem) of augmenting G by a smallest number of new edges so that the resulting graph ˆ G satisfies δG ˆ(X) ≥ r(W1, W2
Results 1  10
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2,794