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149
A Static 2Approximation Algorithm for Vertex Connectivity and Imcremental Approximation Algorithms for Edge and Vertex Connectivity
 J. Algorithms
, 1995
"... . This paper presents insertionsonly algorithms for maintaining the exact and/or approximate size of the minimum edge cut and the minimum vertex cut of a graph. The algorithms output the approximate or exact size k in time O(1) and a cut of size k in time linear in its size. For the minimum edge cu ..."
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Cited by 7 (1 self)
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. This paper presents insertionsonly algorithms for maintaining the exact and/or approximate size of the minimum edge cut and the minimum vertex cut of a graph. The algorithms output the approximate or exact size k in time O(1) and a cut of size k in time linear in its size. For the minimum edge
Dynamic Bottleneck Optimization for 2Vertex and Strong Connectivity
 IN: PROCEEDINGS OF THE 2ND BALKAN CONFERENCE IN INFORMATICS (BCI
, 2005
"... On a complete weighted graph that changes dynamically by edge weight updates, we consider the problem of maintaining efficiently a minimum value b, such that the set of edges with weights less than b induces a 2vertex connected graph (in the undirected case) and a strongly connected graph (in the d ..."
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Cited by 1 (1 self)
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On a complete weighted graph that changes dynamically by edge weight updates, we consider the problem of maintaining efficiently a minimum value b, such that the set of edges with weights less than b induces a 2vertex connected graph (in the undirected case) and a strongly connected graph (in
An Iterative Rounding 2Approximation Algorithm for the Element Connectivity Problem
 In 42nd Annual IEEE Symposium on Foundations of Computer Science
, 2001
"... In the edge connected version of this problem (ECSNDP), these paths must be edgedisjoint. In the vertex connected version of the problem (VCSNDP), the paths must be vertex disjoint. Jain et al. [12] propose a version of the problem intermediate in difficulty to these two, called the element conne ..."
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Cited by 26 (2 self)
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In the edge connected version of this problem (ECSNDP), these paths must be edgedisjoint. In the vertex connected version of the problem (VCSNDP), the paths must be vertex disjoint. Jain et al. [12] propose a version of the problem intermediate in difficulty to these two, called the element
A polylogarithimic approximation algorithm for edgedisjoint paths with congestion 2
 IN PROC. OF IEEE FOCS
, 2012
"... In the EdgeDisjoint Paths with Congestion problem (EDPwC), we are given an undirected nvertex graph G, a collection M = {(s1, t1),..., (sk, tk)} of demand pairs and an integer c. The goal is to connect the maximum possible number of the demand pairs by paths, so that the maximum edge congestion ..."
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Cited by 10 (3 self)
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of the problem. This matches the Ω ( √ n) lower bound on the integrality gap of this relaxation. We show an O(poly log k)approximation algorithm for EDPwC with congestion c = 2, by rounding the same multicommodity flow relaxation. This gives the best possible congestion for a subpolynomial approximation
Faster Vertex Connectivity Algorithms
 Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science.  15
"... We present a preflowpush algorithm for determining the vertex connectivity of an nnode, medge graph with positive vertex capacities. We give a deterministic algorithm that computes (u) = min v 6=u (u; v) in time O(mn log n), where (u; v) is the capacity of the minimum vertex cut between u and v ..."
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Cited by 2 (0 self)
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and v. This leads to a deterministic algorithm for computing in time O(knm log n) and a MonteCarlo algorithm with expected time O(nm log 2 n), where k is the number of nodes in a minimum vertex cut. 1 Introduction Vertex connectivity and edge connectivity problems and algorithms are closely
Algorithms for SingleSource Vertex Connectivity
"... In the Survivable Network Design Problem (SNDP) the goal is to find a minimum cost subset of edges that satisfies a given set of pairwise connectivity requirements among the vertices. This general network design framework has been studied extensively and is tied to the development of major algorithm ..."
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Cited by 25 (2 self)
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algorithmic techniques. For the edgeconnectivity version of the problem, a 2approximation algorithm is known for arbitrary pairwise connectivity requirements. However, no nontrivial algorithms are known for its vertex connectivity counterpart. In fact, even highly restricted special cases of the vertex
Distributed 2vertex connectivity test of graphs using local knowledge
 In Proceeding of the International Conference on Parallel and Distributed Computing Systems
, 2007
"... Abstract — The vertex connectivity of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. This work is devoted to the problem of vertex connectivity test of graphs in a distributed environment based on a general and a constructive approach. The contribu ..."
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Cited by 2 (0 self)
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is the implementation of this protocol in the message passing model. For a given graph G, where M is the number of its edges, N the number of its nodes and Δ is its degree, our algorithms need the following requirements: The first one uses O(Δ×N 2) steps and O(Δ×log Δ) bits per node. The second one uses O(Δ × N 2
1 A New Graph Model with Random Edge Values: Connectivity and Diameter
"... Abstract—We introduce a new random graph model. In our model, n, n ≥ 2, vertices choose a subset of potential edges by considering the (estimated) benefits or utilities of the edges. More precisely, each vertex selects k, k ≥ 1, incident edges it wishes to set up, and an edge between two vertices is ..."
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is present in the graph if and only if both of the end vertices choose the edge. First, we examine the scaling law of the smallest k needed for graph connectivity with increasing n and prove that it is Θ(log(n)). Second, we study the diameter of the random graph when it is connected and demonstrate that
A New Random Graph Model with SelfOptimizing Nodes: Connectivity and Diameter
"... We introduce a new random graph model. In our model, n, n ≥ 2, vertices choose a subset of potential edges by considering the (estimated) benefits or utilities of the edges. More precisely, each vertex selects k, k ≥ 1, incident edges it wishes to set up, and an edge between two vertices is present ..."
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in the graph if and only if both of the end vertices choose the edge. First, we examine the scaling law of the smallest k needed for graph connectivity with increasing n and prove that it is Θ(log(n)). Second, we study the diameter of the random graph and demonstrate that, under certain conditions on k
Power Optimization in FaultTolerant Topology Control Algorithms for Wireless Multihop Networks
 in Proceedings of the 9th Annual International Conference on Mobile Computing and Networking. 2003
, 2003
"... In ad hoc wireless networks, it is crucial to minimize power consumption while maintaining key network properties. This work studies power assignments of wireless devices that minimize power while maintaining kfault tolerance. Specifically, we require all links established by this power setting be ..."
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Cited by 84 (6 self)
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that the edge lengths of the network graph form a metric. In this case, we present simple and practical distributed algorithms for the cases of 2 and 3connectivity with constant approximation factors. We generalize this algorithm to obtain an O(k 2c+2)approximation for general kconnectivity (2 ≤ c ≤ 4
Results 1  10
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149