Triangle counting serves as a key building block for a set of important graph algorithms in network science. In this paper, we address the IEEE HPEC Static Graph Challenge problem of triangle counting, focusing on obtaining the best parallel performance on a single multicore node. Our implementation uses a linear algebra-based approach to triangle counting that has grown out of work related to our miniTri data analytics miniapplication [1] and our efforts to pose graph algorithms in the language of linear algebra. We leverage KokkosKernels to implement this approach efficiently on multicore architectures. Our performance results are competitive with the fastest known graph traversal-based approaches and are significantly faster than the Graph Challenge reference implementations, up to 670,000 times faster than the C++ reference and 10,000 times faster than the Python reference on a single Intel Haswell node.
The ability to simulate wireless networks at large-scale for meaningful amount of time is considerably lacking in today's network simulators. For this reason, many published work in this area often limit their simulation studies to less than a 1,000 nodes and either over-simplify channel characteristics or perform studies over time scales much less than a day. In this report, we show that one can overcome these limitations and study problems of high practical consequence. This work presents two key contributions to high fidelity simulation of large-scale wireless networks: (a) wireless simulations can be sped up by more than 100X in runtime using ideas from spatial indexing algorithms and clipping of negligible signals and (b) clustering and task-oriented programming paradigm can be used to reduce inter- process communication in a parallel discrete event simulation resulting in a better scaling efficiency.
The Graph BLAS effort to standardize a set of graph algorithms building blocks in terms of linear algebra primitives promises to deliver high performing graph algorithms and greatly impact the analysis of big data. However, there are challenges with this approach, which our data analytics miniapp miniTri exposes. In this paper, we improve upon a previously proposed task-parallel approach to linear algebra-based miniTri formulation, addressing these challenges and describing a Kokkos/Qthreads task-parallel implementation that performs as well or slightly better than the highly optimized, baseline OpenMP data-parallel implementation.
Driven by the importance of relational aspects of data to decision-making, graph algorithms have been developed, based on simplified pairwise relationships, to solve a variety of problems. However, evidence has shown that hypergraphs - generalizations of graphs with (hyper)edges that connect any number of vertices - can better model complex, non-pairwise relationships in data and lead to better informed decisions. In this work, we compare graph and hypergraph models in the context of spectral clustering. For these problems, we demonstrate that hypergraphs are computationally more efficient and can better model complex, non-pairwise relationships for many datasets.
This report describes a new capability for hierarchical task-data parallelism using Sandia's Kokkos and Qthreads, and evaluation of this capability with sparse matrix Cholesky factor- ization and social network triangle enumeration mini-applications. Hierarchical task-data parallelism consists of a collection of tasks with executes-after dependences where each task contains data parallel operations performed on a team of hardware threads. The collection of tasks and dependences form a directed acyclic graph of tasks - a task DAG . Major chal- lenges of this research and development effort include: portability and performance across multicore CPU; manycore Intel Xeon Phi, and NVIDIA GPU architectures; scalability with respect to hardware concurrency and size of the task DAG; and usability of the application programmer interface (API).
It is challenging to obtain scalable HPC performance on real applications, especially for data science applications with irregular memory access and computation patterns. To drive co-design efforts in architecture, system, and application design, we are developing miniapps representative of data science workloads. These in turn stress the state of the art in Graph BLAS-like Graph Algorithm Building Blocks (GABB). In this work, we outline a Graph BLAS-like, linear algebra based approach to miniTri, one such miniapp. We describe a task-based prototype implementation and give initial scalability results.
Numerous applications focus on the analysis of entities and the connections between them, and such data are naturally represented as graphs. In particular, the detection of a small subset of vertices with anomalous coordinated connectivity is of broad interest, for problems such as detecting strange traffic in a computer network or unknown communities in a social network. Eigenspace analysis of large-scale graphs is useful for dimensionality reduction of these large, noisy data sets into a more tractable analysis problem. When performing this sort of analysis across many parallel processes, the data partitioning scheme may have a significant impact on the overall running time. Previous work demonstrated that partitioning based on a sampled subset of edges still yields a substantial improvement in running time. In this work, we study this further, exploring how different sampling strategies, graph community structure, and the vertex degree distribution affect the partitioning quality. We show that sampling is an effective technique when partitioning for data analytics problems with community-like structure.
Koniges, Alice K.; Candadai, Jayashree A.; Kaiser, Hartmut K.; Huck, Kevin H.; Kemp, Jeremy K.; Heller, Thomas H.; Anderson, Matthew A.; Lumsdaine, Andrew L.; Serio, Adrian S.; Wolf, Michael W.; Lelbach, Bryce L.; Brightwell, Ronald B.; Sterling, Thomas S.