GraphBLAST: A High-Performance Linear Algebra-based Graph Framework on the GPU

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address some of these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based on sparse linear algebra, which will allow graph algorithms to be expressed in a performant, succinct, composable and portable manner. In this paper, we examine the performance challenges of a linear-algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in "GraphBLAST", the first high-performance linear algebra-based graph framework on NVIDIA GPUs that is open-source. The results show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model.Comment: 50 pages, 14 figures, 14 table

Geometry-Oblivious FMM for Compressing Dense SPD Matrices

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in $N \log N$ or even $N$ time, where $N$ is the matrix size. Compression requires $N \log N$ storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1

Parallel Write-Efficient Algorithms and Data Structures for Computational Geometry

In this paper, we design parallel write-efficient geometric algorithms that perform asymptotically fewer writes than standard algorithms for the same problem. This is motivated by emerging non-volatile memory technologies with read performance being close to that of random access memory but writes being significantly more expensive in terms of energy and latency. We design algorithms for planar Delaunay triangulation, $k$-d trees, and static and dynamic augmented trees. Our algorithms are designed in the recently introduced Asymmetric Nested-Parallel Model, which captures the parallel setting in which there is a small symmetric memory where reads and writes are unit cost as well as a large asymmetric memory where writes are $\omega$ times more expensive than reads. In designing these algorithms, we introduce several techniques for obtaining write-efficiency, including DAG tracing, prefix doubling, reconstruction-based rebalancing and $\alpha$-labeling, which we believe will be useful for designing other parallel write-efficient algorithms

Cloud computing resource scheduling and a survey of its evolutionary approaches

A disruptive technology fundamentally transforming the way that computing services are delivered, cloud computing offers information and communication technology users a new dimension of convenience of resources, as services via the Internet. Because cloud provides a finite pool of virtualized on-demand resources, optimally scheduling them has become an essential and rewarding topic, where a trend of using Evolutionary Computation (EC) algorithms is emerging rapidly. Through analyzing the cloud computing architecture, this survey first presents taxonomy at two levels of scheduling cloud resources. It then paints a landscape of the scheduling problem and solutions. According to the taxonomy, a comprehensive survey of state-of-the-art approaches is presented systematically. Looking forward, challenges and potential future research directions are investigated and invited, including real-time scheduling, adaptive dynamic scheduling, large-scale scheduling, multiobjective scheduling, and distributed and parallel scheduling. At the dawn of Industry 4.0, cloud computing scheduling for cyber-physical integration with the presence of big data is also discussed. Research in this area is only in its infancy, but with the rapid fusion of information and data technology, more exciting and agenda-setting topics are likely to emerge on the horizon