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GraphChallenge.org triangle counting performance [e-print]

Summary

The rise of graph analytic systems has created a need for new ways to measure and compare the capabilities of graph processing systems. The MIT/Amazon/IEEE Graph Challenge has been developed to provide a well-defined community venue for stimulating research and highlighting innovations in graph analysis software, hardware, algorithms, and systems. GraphChallenge.org provides a wide range of preparsed graph data sets, graph generators, mathematically defined graph algorithms, example serial implementations in a variety of languages, and specific metrics for measuring performance. The triangle counting component of GraphChallenge.org tests the performance of graph processing systems to count all the triangles in a graph and exercises key graph operations found in many graph algorithms. In 2017, 2018, and 2019 many triangle counting submissions were received from a wide range of authors and organizations. This paper presents a performance analysis of the best performers of these submissions. These submissions show that their state-of-the-art triangle counting execution time, Ttri, is a strong function of the number of edges in the graph, Ne, which improved significantly from 2017 (Ttri \approx (Ne/10^8)^4=3) to 2018 (Ttri \approx Ne/10^9) and remained comparable from 2018 to 2019. Graph Challenge provides a clear picture of current graph analysis systems and underscores the need for new innovations to achieve high performance on very large graphs
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Summary

The rise of graph analytic systems has created a need for new ways to measure and compare the capabilities of graph processing systems. The MIT/Amazon/IEEE Graph Challenge has been developed to provide a well-defined community venue for stimulating research and highlighting innovations in graph analysis software, hardware, algorithms, and systems...

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Sparse Deep Neural Network graph challenge

Published in:
IEEE High Performance Extreme Computing Conf., HPEC, 24-26 September 2019.

Summary

The MIT/IEEE/Amazon GraphChallenge.org encourages community approaches to developing new solutions for analyzing graphs and sparse data. Sparse AI analytics present unique scalability difficulties. The proposed Sparse Deep Neural Network (DNN) Challenge draws upon prior challenges from machine learning, high performance computing, and visual analytics to create a challenge that is reflective of emerging sparse AI systems. The Sparse DNN Challenge is based on a mathematically well-defined DNN inference computation and can be implemented in any programming environment. Sparse DNN inference is amenable to both vertex-centric implementations and array-based implementations (e.g., using the GraphBLAS.org standard). The computations are simple enough that performance predictions can be made based on simple computing hardware models. The input data sets are derived from the MNIST handwritten letters. The surrounding I/O and verification provide the context for each sparse DNN inference that allows rigorous definition of both the input and the output. Furthermore, since the proposed sparse DNN challenge is scalable in both problem size and hardware, it can be used to measure and quantitatively compare a wide range of present day and future systems. Reference implementations have been implemented and their serial and parallel performance have been measured. Specifications, data, and software are publicly available at GraphChallenge.org.
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Summary

The MIT/IEEE/Amazon GraphChallenge.org encourages community approaches to developing new solutions for analyzing graphs and sparse data. Sparse AI analytics present unique scalability difficulties. The proposed Sparse Deep Neural Network (DNN) Challenge draws upon prior challenges from machine learning, high performance computing, and visual analytics to create a challenge that is...

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Subgraph Detection

Author:
Published in:
Graph Algorithms in the Language of Linear Algebra, pp. 115-133.

Summary

Detecting subgraphs of interest in larger graphs is the goal of many graph analysis techniques. The basis of detection theory is computing the probability of a “foreground” with respect to a model of the “background” data. Hidden Markov Models represent one possible foreground model for patterns of interaction in a graph. Likewise, Kronecker graphs are one possible model for power law background graphs. Combining these models allows estimates of the signal to noise ratio, probability of detection, and probability of false alarm for different classes of vertices in the foreground. These estimates can then be used to construct filters for computing the probability that a background graph contains a particular foreground graph. This approach is applied to the problem of detecting a partially labeled tree graph in a power law background graph. One feature of this method is the ability to a priori estimate the number of vertices that will be detected via the filter.
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Summary

Detecting subgraphs of interest in larger graphs is the goal of many graph analysis techniques. The basis of detection theory is computing the probability of a “foreground” with respect to a model of the “background” data. Hidden Markov Models represent one possible foreground model for patterns of interaction in a...

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Visualizing Large Kronecker Graphs

Published in:
Graph Algorithms in the Language of Linear Algebra, pp. 241-250.

Summary

Kronecker graphs have been shown to be one of the most promising models for real-world networks. Visualization of Kronecker graphs is an important challenge. This chapter describes an interactive framework to assist scientists and engineers in generating, analyzing, and visualizing Kronecker graphs with as little effort as possible.
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Summary

Kronecker graphs have been shown to be one of the most promising models for real-world networks. Visualization of Kronecker graphs is an important challenge. This chapter describes an interactive framework to assist scientists and engineers in generating, analyzing, and visualizing Kronecker graphs with as little effort as possible.

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The Kronecker theory of power law graphs

Author:
Published in:
Graph Algorithms in the Language of Linear Algebra, pp. 205-220.

Summary

An analytical theory of power law graphs is presented based on the Kronecker graph generation technique. Explicit, stochastic, and instance Kronecker graphs are used to highlight different properties. The analysis uses Kronecker exponentials of complete bipartite graphs to formulate the substructure of such graphs. The Kronecker theory allows various high-level quantities (e.g., degree distribution, betweenness centrality, diameter, eigenvalues, and iso-parametric ratio) to be computed directly from the model parameters.
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Summary

An analytical theory of power law graphs is presented based on the Kronecker graph generation technique. Explicit, stochastic, and instance Kronecker graphs are used to highlight different properties. The analysis uses Kronecker exponentials of complete bipartite graphs to formulate the substructure of such graphs. The Kronecker theory allows various high-level...

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Fundamental Questions in the Analysis of Large Graphs

Summary

Graphs are a general approach for representing information that spans the widest possible range of computing applications. They are particularly important to computational biology, web search, and knowledge discovery. As the sizes of graphs increase, the need to apply advanced mathematical and computational techniques to solve these problems is growing dramatically. Examining the mathematical and computational foundations of the analysis of large graphs generally leads to more questions than answers. This book concludes with a discussion of some of these questions.
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Summary

Graphs are a general approach for representing information that spans the widest possible range of computing applications. They are particularly important to computational biology, web search, and knowledge discovery. As the sizes of graphs increase, the need to apply advanced mathematical and computational techniques to solve these problems is growing...

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3-d graph processor

Summary

Graph algorithms are used for numerous database applications such as analysis of financial transactions, social networking patterns, and internet data. While graph algorithms can work well with moderate size databases, processors often have difficulty providing sufficient throughput when the databases are large. This is because the processor architectures are poorly matched to the graph computational flow. For example, most modern processors utilize cache based memory in order to take advantage of highly localized memory access patterns. However, memory access patterns associated with graph processing are often random in nature and can result in high cache miss rates. In addition, graph algorithms require significant overhead computation for dealing with indices of vertices and edges.
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Summary

Graph algorithms are used for numerous database applications such as analysis of financial transactions, social networking patterns, and internet data. While graph algorithms can work well with moderate size databases, processors often have difficulty providing sufficient throughput when the databases are large. This is because the processor architectures are poorly...

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Analytic theory of power law graphs

Author:
Published in:
SIAM Conference on Parallel Processing for Scientific Computing

Summary

An analytical theory of power law graphs is presented basedon the Kronecker graph generation technique. The analysisuses Kronecker exponentials of complete bipartite graphsto formulate the sub-structure of such graphs. This allows various high level quantities (e.g. degree distribution,betweenness centrality, diameter, eigenvalues, and isoparametric ratio) to be computed directly from the model pa-rameters. The implications of this work on “clustering”and “dendragram” heuristics are also discussed.
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Summary

An analytical theory of power law graphs is presented basedon the Kronecker graph generation technique. The analysisuses Kronecker exponentials of complete bipartite graphsto formulate the sub-structure of such graphs. This allows various high level quantities (e.g. degree distribution,betweenness centrality, diameter, eigenvalues, and isoparametric ratio) to be computed directly from the...

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