U Kang

PEGASUS: A Peta-Scale Graph Mining System Implementation and Observations

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.

DOULION: counting triangles in massive graphs with a coin

Counting the number of triangles in a graph is a beautiful algorithmic problem which has gained importance over the last years due to its significant role in complex network analysis. Metrics frequently computed such as the clustering coefficient and the transitivity ratio involve the execution of a triangle counting algorithm. Furthermore, several interesting graph mining applications rely on computing the number of triangles in the graph of interest. In this paper, we focus on the problem of counting triangles in a graph. We propose a practical method, out of which all triangle counting algorithms can potentially benefit. Using a straightforward triangle counting algorithm as a black box, we performed 166 experiments on real-world networks and on synthetic datasets as well, where we show that our method works with high accuracy, typically more than 99% and gives significant speedups, resulting in even ≈ 130 times faster performance.

PEGASUS: mining peta-scale graphs

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.

GBASE: a scalable and general graph management system

Graphs appear in numerous applications including cyber-security, the Internet, social networks, protein networks, recommendation systems, and many more. Graphs with millions or even billions of nodes and edges are common-place. How to store such large graphs efficiently? What are the core operations/queries on those graph? How to answer the graph queries quickly? We propose GBASE, a scalable and general graph management and mining system. The key novelties lie in 1) our storage and compression scheme for a parallel setting and 2) the carefully chosen graph operations and their efficient implementation. We designed and implemented an instance of GBASE using MapReduce/Hadoop. GBASE provides a parallel indexing mechanism for graph mining operations that both saves storage space, as well as accelerates queries. We ran numerous experiments on real graphs, spanning billions of nodes and edges, and we show that our proposed GBASE is indeed fast, scalable and nimble, with significant savings in space and time.

HADI: Mining Radii of Large Graphs

Given large, multimillion-node graphs (e.g., Facebook, Web-crawls, etc.), how do they evolve over time? How are they connected? What are the central nodes and the outliers? In this article we define the Radius plot of a graph and show how it can answer these questions. However, computing the Radius plot is prohibitively expensive for graphs reaching the planetary scale. There are two major contributions in this article: (a) We propose HADI (HAdoop DIameter and radii estimator), a carefully designed and fine-tuned algorithm to compute the radii and the diameter of massive graphs, that runs on the top of the Hadoop/MapReduce system, with excellent scale-up on the number of available machines (b) We run HADI on several real world datasets including YahooWeb (6B edges, 1/8 of a Terabyte), one of the largest public graphs ever analyzed. Thanks to HADI, we report fascinating patterns on large networks, like the surprisingly small effective diameter, the multimodal/bimodal shape of the Radius plot, and its palindrome motion over time.

Big graph mining: algorithms and discoveries

How do we find patterns and anomalies in very large graphs with billions of nodes and edges? How to mine such big graphs efficiently? Big graphs are everywhere, ranging from social networks and mobile call networks to biological networks and the World Wide Web. Mining big graphs leads to many interesting applications including cyber security, fraud detection, Web search, recommendation, and many more. In this paper we describe Pegasus, a big graph mining system built on top of MapReduce, a modern distributed data processing platform. We introduce GIM-V, an important primitive that Pegasus uses for its algorithms to analyze structures of large graphs. We also introduce HEigen, a large scale eigensolver which is also a part of Pegasus. Both GIM-V and HEigen are highly optimized, achieving linear scale up on the number of machines and edges, and providing 9.2x and 76x faster performance than their naive counterparts, respectively. Using Pegasus, we analyze very large, real world graphs with billions of nodes and edges. Our findings include anomalous spikes in the connected component size distribution, the 7 degrees of separation in a Web graph, and anomalous adult advertisers in the who-follows-whom Twitter social network.

Mining large graphs: Algorithms, inference, and discoveries

How do we find patterns and anomalies, on graphs with billions of nodes and edges, which do not fit in memory? How to use parallelism for such terabyte-scale graphs? In this work, we focus on inference, which often corresponds, intuitively, to “guilt by association” scenarios. For example, if a person is a drug-abuser, probably its friends are so, too; if a node in a social network is of male gender, his dates are probably females. We show how to do inference on such huge graphs through our proposed HAdoop Line graph Fixed Point (Ha-Lfp), an efficient parallel algorithm for sparse billion-scale graphs, using the Hadoop platform. Our contributions include (a) the design of Ha-Lfp, observing that it corresponds to a fixed point on a line graph induced from the original graph; (b) scalability analysis, showing that our algorithm scales up well with the number of edges, as well as with the number of machines; and (c) experimental results on two private, as well as two of the largest publicly available graphs — the Web Graphs from Yahoo! (6.6 billion edges and 0.24 Tera bytes), and the Twitter graph (3.7 billion edges and 0.13 Tera bytes). We evaluated our algorithm using M45, one of the top 50 fastest supercomputers in the world, and we report patterns and anomalies discovered by our algorithm, which would be invisible otherwise.

Unifying Guilt-by-association approaches: theorems and fast algorithms

If several friends of Smith have committed petty thefts, what would you say about Smith? Most people would not be surprised if Smith is a hardened criminal. Guilt-by-association methods combine weak signals to derive stronger ones, and have been extensively used for anomaly detection and classification in numerous settings (e.g., accounting fraud, cyber-security, calling-card fraud). The focus of this paper is to compare and contrast several very successful, guilt-by-association methods: Random Walk with Restarts, Semi-Supervised Learning, and Belief Propagation (BP). Our main contributions are two-fold: (a) theoretically, we prove that all the methods result in a similar matrix inversion problem; (b) for practical applications, we developed FaBP, a fast algorithm that yields 2× speedup, equal or higher accuracy than BP, and is guaranteed to converge. We demonstrate these benefits using synthetic and real datasets, including YahooWeb, one of the largest graphs ever studied with BP.

HEigen: Spectral Analysis for Billion-Scale Graphs

Given a graph with billions of nodes and edges, how can we find patterns and anomalies? Are there nodes that participate in too many or too few triangles? Are there close-knit near-cliques? These questions are expensive to answer unless we have the first several eigenvalues and eigenvectors of the graph adjacency matrix. However, eigensolvers suffer from subtle problems (e.g., convergence) for large sparse matrices, let alone for billion-scale ones. We address this problem with the proposed HEIGEN algorithm, which we carefully design to be accurate, efficient, and able to run on the highly scalable MAPREDUCE (HADOOP) environment. This enables HEIGEN to handle matrices more than 1;000 × larger than those which can be analyzed by existing algorithms. We implement HEIGEN and run it on the M45 cluster, one of the top 50 supercomputers in the world. We report important discoveries about nearcliques and triangles on several real-world graphs, including a snapshot of the Twitter social network (56 Gb, 2 billion edges) and the “YahooWeb” data set, one of the largest publicly available graphs (120 Gb, 1.4 billion nodes, 6.6 billion edges).

gbase: an efficient analysis platform for large graphs

Graphs appear in numerous applications including cyber security, the Internet, social networks, protein networks, recommendation systems, citation networks, and many more. Graphs with millions or even billions of nodes and edges are common-place. How to store such large graphs efficiently? What are the core operations/queries on those graph? How to answer the graph queries quickly? We propose Gbase, an efficient analysis platform for large graphs. The key novelties lie in (1) our storage and compression scheme for a parallel, distributed settings and (2) the carefully chosen graph operations and their efficient implementations. We designed and implemented an instance of Gbase using Mapreduce/Hadoop. Gbase provides a parallel indexing mechanism for graph operations that both saves storage space, as well as accelerates query responses. We run numerous experiments on real and synthetic graphs, spanning billions of nodes and edges, and we show that our proposed Gbase is indeed fast, scalable, and nimble, with significant savings in space and time.