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1,459
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 res ..."
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Cited by 524 (19 self)
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tensions. 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 this way
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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and ap proximately 4000 findin nodes, with a number of ob served findings that varies per case. Due to the form of the noisyor CPTs the complexity of inference is ex ponential in the number of positive findings Results Initial experiments The experimental protocol for the PYRAMID network was as follows
Complex Behavior at Scale: An Experimental Study of LowPower Wireless Sensor Networks
, 2002
"... A new class of networked systems is emerging that involve very large numbers of small, lowpower, wireless devices. We present findings from a large scale empirical study involving over 150 such nodes operated at various transmission power settings. The instrumentation in our experiments permits us ..."
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Cited by 303 (35 self)
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A new class of networked systems is emerging that involve very large numbers of small, lowpower, wireless devices. We present findings from a large scale empirical study involving over 150 such nodes operated at various transmission power settings. The instrumentation in our experiments permits us
Graph evolution: Densification and shrinking diameters
 ACM TKDD
, 2007
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 267 (16 self)
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heavy tails for in and outdegree distributions, communities, smallworld phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs
Stimulusselective properties of inferior temporal neurons in the macaque
 J. Neurosci
, 1984
"... Previous studies have reported that some neurons in the inferior temporal (IT) cortex respond selectively to highly specific complex objects. In the present study, we conducted the first systematic survey of the responses of IT neurons to both simple stimuli, such as edges and bars, and highly compl ..."
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Cited by 236 (5 self)
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, stimulusselective cells were often selective along the dimensions of shape, color, or texture of a stimulus, and this selectivity was maintained throughout a large receptive field. Although most IT neurons do not appear to be “detectors ” for complex objects, we did find a separate population of cells
Social Network Analysis for Routing in Disconnected Delaytolerant MANETs
, 2007
"... Message delivery in sparse Mobile Ad hoc Networks (MANETs) is difficult due to the fact that the network graph is rarely (if ever) connected. A key challenge is to find a route that can provide good delivery performance and low endtoend delay in a disconnected network graph where nodes may move fr ..."
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Cited by 276 (1 self)
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Message delivery in sparse Mobile Ad hoc Networks (MANETs) is difficult due to the fact that the network graph is rarely (if ever) connected. A key challenge is to find a route that can provide good delivery performance and low endtoend delay in a disconnected network graph where nodes may move
Finding small balanced separators
, 2006
"... Let G be an nvertex graph that has a vertex separator of size k that partitions the graph into connected components of size smaller than αn, for some fixed 2/3 ≤ α < 1. Such a separator is called an αseparator. Finding an αseparator of size at most k is NPhard. Moreover, under reasonable comp ..."
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Cited by 12 (0 self)
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complexity theoretic assumptions, it is shown that this problem is not polynomially solvable even when k = O(log n). In this paper, we give a randomized algorithm that finds an αseparator of size k in the given graph, unless the graph contains an (α + ɛ)separator of size strictly less than k, in which case
Spectral partitioning works: planar graphs and finite element meshes, in:
 Proceedings of the 37th Annual Symposium on Foundations of Computer Science,
, 1996
"... Abstract Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to wo ..."
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Cited by 201 (10 self)
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Abstract Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment
Complex contagion and the weakness of long ties
, 2005
"... Complex Contagion and the Weakness of Long Ties The strength of weak ties is that they tend to be long – they connect socially distant locations. Recent research on “small worlds ” shows that remarkably few long ties are needed to give large and highly clustered populations the “degrees of separatio ..."
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Cited by 165 (9 self)
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Complex Contagion and the Weakness of Long Ties The strength of weak ties is that they tend to be long – they connect socially distant locations. Recent research on “small worlds ” shows that remarkably few long ties are needed to give large and highly clustered populations the “degrees
Analysis of multilevel graph partitioning
, 1995
"... Recently, a number of researchers have investigated a class of algorithms that are based on multilevel graph partitioning that have moderate computational complexity, and provide excellent graph partitions. However, there exists little theoretical analysis that could explain the ability of multileve ..."
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Cited by 106 (12 self)
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factor. We also show that the size of a good vertexseparator of the coarse graph projected to the finer graph (without performing refinement in the uncoarsening phase) is higher than the size of a good vertexseparator of the finer graph by at most a small factor.
Results 1  10
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