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LowDiameter Graph Decomposition is in NC
, 1992
"... We obtain the first NC algorithm for the lowdiameter graph decomposition problem on arbitrary graphs. Our algorithm runs in O(log 5 (n)) time, and uses O(n 2 ) processors. 1 Introduction For an undirected graph G = (V; E), a (Ø; d)decomposition is defined to be a Øcoloring of the nodes of th ..."
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Cited by 3 (1 self)
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We obtain the first NC algorithm for the lowdiameter graph decomposition problem on arbitrary graphs. Our algorithm runs in O(log 5 (n)) time, and uses O(n 2 ) processors. 1 Introduction For an undirected graph G = (V; E), a (Ø; d)decomposition is defined to be a Øcoloring of the nodes
Building LowDiameter P2P Networks
, 2001
"... In a peertopeer (P2P) network, nodes connect into an existing network and participate in providing and availing of services. There is no dichotomy between a central server and distributed clients. Current P2P networks (e.g., Gnutella) are constructed by participants following their own uncoordina ..."
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Cited by 126 (3 self)
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that it results in connected networks of constant degree and logarithmic diameter. It does so with no global knowledge of all the nodes in the network. In the most common P2P application to date (search), these properties are crucial.
On Straightening LowDiameter Unit Trees
 In Proc. 13th International Symposium on Graph Drawing
, 2005
"... A polygonal chain is a sequence of consecutively joined edges embedded in space. A kchain is a chain of k edges. A polygonal tree is a set of edges joined into a tree structure embedded in space. A unit tree is a tree with only edges of unit length. A chain or a tree is simple if nonadjacent edges ..."
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Cited by 7 (2 self)
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common straight line such that each edge points “away ” from a designed leaf node. Otherwise it is called locked. Graph reconfiguration problems have wide applications in contexts including robotics, molecular conformation, rigidity and knot theory. The motivation for us to study unit trees
The geometry of graphs and some of its algorithmic applications
 Combinatorica
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that r ..."
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Cited by 543 (20 self)
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extensions. 0 For graphs embeddable in lowdimensional spaces with a small distortion, we can find lowdiameter decompositions (in the sense of [4] and [34]). The parameters of the decomposition depend only on the dimension and the distortion and not on the size of the graph. 0 In graphs embedded
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Finding LowDiameter, Low EdgeCost, Networks
, 1997
"... This paper describes a simulated annealing algorithm to compute kconnected graphs that minimize a linear combination of graph edgecost and diameter. Replicas of Internet information services can use graphs with these properties to propagate updates among themselves. We report the algorithm's ..."
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Cited by 4 (0 self)
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. When optimizing edgecost only, the resulting graphs show 25 and 30% reductions edgecost and diameter, respectively. 1 Introduction This paper describes a simulated annealing algorithm to construct low diameter, low edgecost, 2 and 3connected graphs. We need graphs with these properties
Embedding of Tree Networks into Hypercubes
, 1985
"... The hypercube is a good host graph for the embedding of networks of processors because of its low degree and low diameter. Graphs such as trees and arrays can be embedded into a hypercube with small dilation and expansion costs, but there are classes of graphs which can be embedded into a hypercube ..."
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Cited by 29 (0 self)
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The hypercube is a good host graph for the embedding of networks of processors because of its low degree and low diameter. Graphs such as trees and arrays can be embedded into a hypercube with small dilation and expansion costs, but there are classes of graphs which can be embedded into a hypercube
Integration: Reaching Consensus in LowDiameter Wireless Networks
"... In a centrally controlled system consensus is often reached by decree: the central entity in charge ofthe system dictates the "consensus " to the rankandfile. The situation is vastly different in a truly decentralized distributed system where the various entities in the system mu ..."
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to all situations where a consensus must be reached by anonymous participants (whoperhaps do not wish to reveal their identities) provided that the underlying graph has low diameter. 1.
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