Graphs and networks are used to model interactions in a variety of contexts. There is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure. Some of the most useful metrics are triangle-based and give a measure of the connectedness of mutual friends. This is often summarized in terms of clustering coefficients, which measure the likelihood that two neighbors of a node are themselves connected. Computing these measures exactly for large-scale networks is prohibitively expensive in both memory and time. However, a recent wedge-sampling algorithm has proved successful in efficiently and accurately estimating clustering coefficients. In this paper, we describe how to implement this approach in MapReduce to deal with massive graphs. We show results on publicly available networks, the largest of which is 132M nodes and 4.7B edges, as well as artificially generated networks (using the Graph500 benchmark), the largest of which has 240M nodes and 8.5B edges...
MapReduce has been used for network and graph analysis in a variety of contexts. It is a natural choice, if for no other reason than the fact that it is widely deployed @cite_60 . Pegasus @cite_26 is a general library for large-scale graph processing; the largest graph they considered was 1.4M vertices and 6.6M edges and the PageRank analytic, but they did not report execution times. Lin and Schatz @cite_50 propose some special techniques for graph algorithms such as PageRank that depend on matrix-vector products. MapReduce sampling-based techniques that reduce the overall graph size are discussed by @cite_0 .
@cite_0 @cite_26 @cite_50 @cite_60
2167927436 2095223744 2067005380 2020302654
In this paper, we describe PEGASUS, an open source Peta Graph Mining library which performs typical graph mining tasks such as computing the diameter of the graph, computing the radius of each node and finding the connected components. As the size of graphs reaches several Giga-, Tera- or Peta-bytes, the necessity for such a library grows too. To the best of our knowledge, PEGASUS is the first such library, implemented on the top of the Hadoop platform, the open source version of MapReduce. Many graph mining operations (PageRank, spectral clustering, diameter estimation, connected components etc.) are essentially a repeated matrix-vector multiplication. In this paper we describe a very important primitive for PEGASUS, called GIM-V (Generalized Iterated Matrix-Vector multiplication). GIM-V is highly optimized, achieving (a) good scale-up on the number of available machines (b) linear running time on the number of edges, and (c) more than 5 times faster performance over the non-optimized version of GIM-V. Our experiments ran on M45, one of the top 50 supercomputers in the world. We report our findings on several real graphs, including one of the largest publicly available Web Graphs, thanks to Yahoo!, with 6,7 billion edges. In this paper, we describe PeGaSus, an open source Peta Graph Mining library which performs typical graph mining tasks such as computing the diameter of the graph, computing the radius of each node, finding the connected components, and computing the importance score of nodes. As the size of graphs reaches several Giga-, Tera- or Peta-bytes, the necessity for such a library grows too. To the best of our knowledge, PeGaSus is the first such library, implemented on the top of the Hadoop platform, the open source version of MapReduce. Many graph mining operations (PageRank, spectral clustering, diameter estimation, connected components, etc.) are essentially a repeated matrix-vector multiplication. In this paper, we describe a very important primitive for PeGaSus, called GIM-V (generalized iterated matrix-vector multiplication). GIM-V is highly optimized, achieving (a) good scale-up on the number of available machines, (b) linear running time on the number of edges, and (c) more than 5 times faster performance over the non-optimized version of GIM-V. Our experiments ran on M45, one of the top 50 supercomputers in the world. We report our findings on several real graphs, including one of the largest publicly available Web graphs, thanks to Yahoo!, with ≈ 6.7 billion edges. MapReduce is becoming the state-of-the-art computing paradigm for processing large-scale datasets on a large cluster with tens or thousands of nodes. It has been widely used in various fields such as e-commerce, Web search, social networks, and scientific computation. Understanding the characteristics of MapReduce workloads is the key to achieving better configuration decisions and improving the system throughput. However, workload characterization of MapReduce, especially in a large-scale production environment, has not been well studied yet. To gain insight on MapReduce workloads, we collected a two-week workload trace from a 2,000-node Hadoop cluster at Taobao, which is the biggest online e-commerce enterprise in Asia, ranked 14th in the world as reported by Alexa. The workload trace covered 912,157 jobs, logged from Dec. 4 to Dec. 20, 2011. We characterized the workload at the granularity of job and task, respectively and concluded with a set of interesting observations. The results of workload characterization are representative and generally consistent with data platforms for e-commerce websites, which can help other researchers and engineers understand the performance and job characteristics of Hadoop in their production environments. In addition, we use these job analysis statistics to derive several implications for potential performance optimization solutions. Graphs are analyzed in many important contexts, including ranking search results based on the hyperlink structure of the world wide web, module detection of proteinprotein interaction networks, and privacy analysis of social networks. Many graphs of interest are difficult to analyze because of their large size, often spanning millions of vertices and billions of edges. As such, researchers have increasingly turned to distributed solutions. In particular, MapReduce has emerged as an enabling technology for large-scale graph processing. However, existing best practices for MapReduce graph algorithms have significant shortcomings that limit performance, especially with respect to partitioning, serializing, and distributing the graph. In this paper, we present three design patterns that address these issues and can be used to accelerate a large class of graph algorithms based on message passing, exemplified by PageRank. Experiments show that the application of our design patterns reduces the running time of PageRank on a web graph with 1.4 billion edges by 69 .