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.

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. Twitter's 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.

We present the design and testing of an algorithm for iterative refinement of the solution of linear equations where the residual is computed with extra precision. This algorithm was originally proposed in 1948 and analyzed in the 1960s as a means to compute very accurate solutions to all but the most ill-conditioned linear systems. However, two obstacles have until now prevented its adoption in standard subroutine libraries like LAPACK: (1) There was no standard way to access the higher precision arithmetic needed to compute residuals, and (2) it was unclear how to compute a reliable error bound for the computed solution. The completion of the new BLAS Technical Forum Standard has essentially removed the first obstacle. To overcome the second obstacle, we show how the application of iterative refinement can be used to compute an error bound in any norm at small cost and use this to compute both an error bound in the usual infinity norm, and a componentwise relative error bound.We report extensive test results on over 6.2 million matrices of dimensions 5, 10, 100, and 1000. As long as a normwise (componentwise) condition number computed by the algorithm is less than 1/max{10,√n}ε_w, the computed normwise (componentwise) error bound is at most 2 max{10,√n} · ε_w, and indeed bounds the true error. Here,nis the matrix dimension and ε_w= 2^-24is the working precision. Residuals were computed in double precision (53 bits of precision). In other words, the algorithm always computed a tiny error at negligible extra cost for most linear systems. For worse conditioned problems (which we can detect using condition estimation), we obtained small correct error bounds in over 90% of cases.

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.

The volume of existing graph-structured data requires improved parallel tools and algorithms. Finding communities, smaller sub graphs densely connected within the sub graph than to the rest of the graph, plays a role both in developing new parallel algorithms as well as opening smaller portions of the data to current analysis tools. We improve performance of our parallel community detection algorithm by 20% on the massively multithreaded Cray XMT, evaluate its performance on the next-generation Cray XMT2, and extend its reach to Intel-based platforms with OpenMP. To our knowledge, not only is this the first massively parallel community detection algorithm but also the only such algorithm that achieves excellent performance and good parallel scalability across all these platforms. Our implementation analyzes a moderate sized graph with 105 million vertices and 3.3 billion edges in around 500 seconds on a four processor, 80-logical-core Intel-based system and 1100 seconds on a 64-processor Cray XMT2.