Results 1  10
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27
On the Eigenvalue Power Law
 Proc. of the 6th International Workshop on Randomization and Approximation Techniques
, 2002
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ThreeDimensional Orthogonal Graph Drawing
, 2000
"... vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . ..."
Abstract

Cited by 33 (13 self)
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vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv I Orthogonal Graph Drawing 1 1
PROBABILISTIC METHODS IN GROUP THEORY
, 1965
"... The application of probabilistic methods to another chapter of mathematics (number theory, different branches of analysis, graph theory etc.) has in the last 30 years often led to interesting results, which could not be obtained by the usual methods of the chapters in question. These results are in ..."
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Cited by 27 (0 self)
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The application of probabilistic methods to another chapter of mathematics (number theory, different branches of analysis, graph theory etc.) has in the last 30 years often led to interesting results, which could not be obtained by the usual methods of the chapters in question. These results are in most
A Theorem about the Channel Assignment Problem
, 2001
"... A list channel assignment problem is a triple (G, L, w) where G is a graph, L is a function assigning vertices of G lists of integers (colours) and w is a function assigning edges of G positive integers (weights). A colouring c of the vertices of G is proper if c(v) ∈ L(v) for each vertex v ..."
Abstract

Cited by 27 (5 self)
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A list channel assignment problem is a triple (G, L, w) where G is a graph, L is a function assigning vertices of G lists of integers (colours) and w is a function assigning edges of G positive integers (weights). A colouring c of the vertices of G is proper if c(v) &isin; L(v) for each vertex v and c(u)c(v) &ge; w(uv) for each edge uv. A weighted degree deg_w(v) of a vertex v is the sum of the weights of the edges incident with v. If G is connected, L(v) > deg_w(v) for at least one v and L(v) &ge; deg_w(v) for all v, then a proper colouring always exists.
Advances on the Hamiltonian problem  A survey
, 2002
"... This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonianconnected graphs and digraphs. ..."
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Cited by 21 (0 self)
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This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonianconnected graphs and digraphs.
Coevolution of social and affiliation networks
 In 15th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD
, 2009
"... In our work, we address the problem of modeling social network generation which explains both link and group formation. Recent studies on social network evolution propose generative models which capture the statistical properties of realworld networks related only to nodetonode link formation. We ..."
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Cited by 19 (2 self)
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In our work, we address the problem of modeling social network generation which explains both link and group formation. Recent studies on social network evolution propose generative models which capture the statistical properties of realworld networks related only to nodetonode link formation. We propose a novel model which captures the coevolution of social and affiliation networks. We provide surprising insights into group formation based on observations in several realworld networks, showing that users often join groups for reasons other than their friends. Our experiments show that the model is able to capture both the newly observed and previously studied network properties. This work is the first to propose a generative model which captures the statistical properties of these complex networks. The proposed model facilitates controlled experiments which study the effect of actors ’ behavior on the network evolution, and it allows the generation of realistic synthetic datasets.
Robustness as an Evolutionary Principle
 Proceedings of the Royal Society of London, Series B
, 2000
"... We suggest simulating evolution of complex organisms using... ..."
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Cited by 18 (1 self)
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We suggest simulating evolution of complex organisms using...
Random biochemical networks: the probability of selfsustaining autocatalysis
 Journal of Theoretical Biology
, 2004
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Small Worlds  The Structure of Social Networks
, 1999
"... Experimentally it has been found that any two people in the world, chosen at random, are connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the six degrees of separation, has been the subject of a conside ..."
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Cited by 15 (2 self)
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Experimentally it has been found that any two people in the world, chosen at random, are connected to one another by a short chain of intermediate acquaintances, of typical length about six. This phenomenon, colloquially referred to as the six degrees of separation, has been the subject of a considerable amount of recent research and modeling, which we review here.
On the Representation and Multiplication of Hypersparse Matrices
, 2008
"... Multicore processors are marking the beginning of a new era of computing where massive parallelism is available and necessary. Slightly slower but easy to parallelize kernels are becoming more valuable than sequentially faster kernels that are unscalable when parallelized. In this paper, we focus on ..."
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Cited by 11 (7 self)
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Multicore processors are marking the beginning of a new era of computing where massive parallelism is available and necessary. Slightly slower but easy to parallelize kernels are becoming more valuable than sequentially faster kernels that are unscalable when parallelized. In this paper, we focus on the multiplication of sparse matrices (SpGEMM). We first present the issues with existing sparse matrix representations and multiplication algorithms that make them unscalable to thousands of processors. Then, we develop and analyze two new algorithms that overcome these limitations. We consider our algorithms first as the sequential kernel of a scalable parallel sparse matrix multiplication algorithm and second as part of a polyalgorithm for SpGEMM that would execute different kernels depending on the sparsity of the input matrices. Such a sequential kernel requires a new data structure that exploits the hypersparsity of the individual submatrices owned by a single processor after the 2D partitioning. We experimentally evaluate the performance and characteristics of our algorithms and show that they scale significantly better than existing kernels.