David Ediger

A faster parallel algorithm and efficient multithreaded implementations for evaluating betweenness centrality on massive datasets

We present a new lock-free parallel algorithm for computing betweenness centrality of massive complex networks that achieves better spatial locality compared with previous approaches. Betweenness centrality is a key kernel in analyzing the importance of vertices (or edges) in applications ranging from social networks, to power grids, to the influence of jazz musicians, and is also incorporated into the DARPA HPCS SSCA#2, a benchmark extensively used to evaluate the performance of emerging high-performance computing architectures for graph analytics. We design an optimized implementation of betweenness centrality for the massively multithreaded Cray XMT system with the Thread-storm processor. For a small-world network of 268 million vertices and 2.147 billion edges, the 16-processor XMT system achieves a TEPS rate (an algorithmic performance count for the number of edges traversed per second) of 160 million per second, which corresponds to more than a 2× performance improvement over the previous parallel implementation. We demonstrate the applicability of our implementation to analyze massive real-world datasets by computing approximate betweenness centrality for the large IMDb movie-actor network.

Massive Social Network Analysis: Mining Twitter for Social Good

Social networks produce an enormous quantity of data. Facebook consists of over 400 million active users sharing over 5 billion pieces of information each month. Analyzing this vast quantity of unstructured data presents challenges for software and hardware. We present GraphCT, a Graph Characterization Toolkit for massive graphs representing social network data. On a 128-processor Cray XMT, GraphCT estimates the betweenness centrality of an artificially generated (R-MAT) 537 million vertex, 8.6 billion edge graph in 55 minutes and a real-world graph (Kwak, et al.) with 61.6 million vertices and 1.47 billion edges in 105 minutes. We use GraphCT to analyze public data from Twitter, a microblogging network. Twitters message connections appear primarily tree-structured as a news dissemination system. Within the public data, however, are clusters of conversations. Using GraphCT, we can rank actors within these conversations and help analysts focus attention on a much smaller data subset.

STINGER: High performance data structure for streaming graphs

The current research focus on “big data” problems highlights the scale and complexity of analytics required and the high rate at which data may be changing. In this paper, we present our high performance, scalable and portable software, Spatio-Temporal Interaction Networks and Graphs Extensible Representation (STINGER), that includes a graph data structure that enables these applications. Key attributes of STINGER are fast insertions, deletions, and updates on semantic graphs with skewed degree distributions. We demonstrate a process of algorithmic and architectural optimizations that enable high performance on the Cray XMT family and Intel multicore servers. Our implementation of STINGER on the Cray XMT processes over 3 million updates per second on a scale-free graph with 537 million edges.

Parallel community detection for massive graphs

Tackling the current volume of graph-structured data requires parallel tools. We extend our work on analyzing such massive graph data with the first massively parallel algorithm for community detection that scales to current data sizes, scaling to graphs of over 122 million vertices and nearly 2 billion edges in under 7300 seconds on a massively multithreaded Cray XMT. Our algorithm achieves moderate parallel scalability without sacrificing sequential operational complexity. Community detection partitions a graph into subgraphs more densely connected within the subgraph than to the rest of the graph. We take an agglomerative approach similar to Clauset, Newman, and Moores sequential algorithm, merging pairs of connected intermediate subgraphs to optimize different graph properties. Working in parallel opens new approaches to high performance. On smaller data sets, we find the outputs modularity compares well with the standard sequential algorithms.

Massive streaming data analytics: A case study with clustering coefficients

We present a new approach for parallel massive graph analysis of streaming, temporal data with a dynamic and extensible representation. Handling the constant stream of new data from health care, security, business, and social network applications requires new algorithms and data structures. We examine data structure and algorithm trade-offs that extract the parallelism necessary for high-performance updating analysis of massive graphs. Static analysis kernels often rely on storing input data in a specific structure. Maintaining these structures for each possible kernel with high data rates incurs a significant performance cost. A case study computing clustering coefficients on a general-purpose data structure demonstrates incremental updates can be more efficient than global recomputation. Within this kernel, we compare three methods for dynamically updating local clustering coefficients: a brute-force local recalculation, a sorting algorithm, and our new approximation method using a Bloom filter. On 32 processors of a Cray XMT with a synthetic scale-free graph of 224 ≈ 16 million vertices and 229 ≈ 537 million edges, the brute-force method processes a mean of over 50 000 updates per second and our Bloom filter approaches 200 000 updates per second.

A performance evaluation of open source graph databases

With the proliferation of large, irregular, and sparse relational datasets, new storage and analysis platforms have arisen to fill gaps in performance and capability left by conventional approaches built on traditional database technologies and query languages. Many of these platforms apply graph structures and analysis techniques to enable users to ingest, update, query, and compute on the topological structure of the network represented as sets of edges relating sets of vertices. To store and process Facebook-scale datasets, software and algorithms must be able to support data sources with billions of edges, update rates of millions of updates per second, and complex analysis kernels. These platforms must provide intuitive interfaces that enable graph experts and novice programmers to write implementations of common graph algorithms. In this paper, we conduct a qualitative study and a performance comparison of 12 open source graph databases using four fundamental graph algorithms on networks containing up to 256 million edges.

Tracking Structure of Streaming Social Networks

Current online social networks are massive and still growing. For example, Face book has over 500 million active users sharing over 30 billion items per month. The scale within these data streams has outstripped traditional graph analysis methods. Real-time monitoring for anomalies may require dynamic analysis rather than repeated static analysis. The massive state behind multiple persistent queries requires shared data structures and flexible representations. We present a framework based on the STINGER data structure that can monitor a global property, connected components, on a graph of 16 million vertices at rates of up to 240,000 updates per second on 32 processors of a Cray XMT. For very large scale-free graphs, our implementation uses novel batching techniques that exploit the scale-free nature of the data and run over three times faster than prior methods. Our framework handles, for the first time, real-world data rates, opening the door to higher-level analytics such as community and anomaly detection.

GraphCT: Multithreaded Algorithms for Massive Graph Analysis

The digital world has given rise to massive quantities of data that include rich semantic and complex networks. A social graph, for example, containing hundreds of millions of actors and tens of billions of relationships is not uncommon. Analyzing these large data sets, even to answer simple analytic queries, often pushes the limits of algorithms and machine architectures. We present GraphCT, a scalable framework for graph analysis using parallel and multithreaded algorithms on shared memory platforms. Utilizing the unique characteristics of the Cray XMT, GraphCT enables fast network analysis at unprecedented scales on a variety of input data sets. On a synthetic power law graph with 2 billion vertices and 17 billion edges, we can find the connected components in 2 minutes. We can estimate the betweenness centrality of a similar graph with 537 million vertices and over 8 billion edges in under 1 hour. GraphCT is built for portability and performance.

Generalizing k-Betweenness Centrality Using Short Paths and a Parallel Multithreaded Implementation

We present a new parallel algorithm that extends and generalizes the traditional graph analysis metric of betweenness centrality to include additional non-shortest paths according to an input parameter k. Betweenness centrality is a useful kernel for analyzing the importance of vertices or edges in a graph and has found uses in social networks, biological networks, and power grids, among others. k-betweenness centrality captures the additional information provided by paths whose length is within k units of the shortest path length. These additional paths provide robustness that is not captured in traditional betweenness centrality computations, and they may become important shortest paths if key edges are missing in the data. We implement our parallel algorithm using lock-free methods on a massively multithreaded Cray XMT. We apply this implementation to a real-world data set of pages on the World Wide Web and show the importance of the additional data incorporated by our algorithm.

Investigating Graph Algorithms in the BSP Model on the Cray XMT

Implementing parallel graph algorithms in large, shared memory machines, such as the Cray XMT, can be challenging for programmers. Synchronization, deadlock, hot spotting, and others can be barriers to obtaining linear scalability. Alternative programming models, such as the bulk synchronous parallel programming model used in Googles Pregel, have been proposed for large graph analytics. This model eases programmer complexity by eliminating deadlock and simplifying data sharing. We investigate the algorithmic effects of the BSP model for graph algorithms and compare performance and scalability with hand-tuned, open source software using GraphCT. We analyze the innermost iterations of these algorithms to understand the differences in scalability between BSP and shared memory algorithms. We show that scalable performance can be obtained with graph algorithms in the BSP model on the Cray XMT. These algorithms perform within a factor of 10 of hand-tuned C code.