Graphs, Matrices, and the GraphBLAS: Seven Good Reasons

The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istc- bigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.Comment: 10 pages; International Conference on Computational Science workshop on the Applications of Matrix Computational Methods in the Analysis of Modern Dat

Efficient Implementation of a Synchronous Parallel Push-Relabel Algorithm

Motivated by the observation that FIFO-based push-relabel algorithms are able to outperform highest label-based variants on modern, large maximum flow problem instances, we introduce an efficient implementation of the algorithm that uses coarse-grained parallelism to avoid the problems of existing parallel approaches. We demonstrate good relative and absolute speedups of our algorithm on a set of large graph instances taken from real-world applications. On a modern 40-core machine, our parallel implementation outperforms existing sequential implementations by up to a factor of 12 and other parallel implementations by factors of up to 3

Performance Evaluation of Sparse Matrix Multiplication Kernels on Intel Xeon Phi

Intel Xeon Phi is a recently released high-performance coprocessor which features 61 cores each supporting 4 hardware threads with 512-bit wide SIMD registers achieving a peak theoretical performance of 1Tflop/s in double precision. Many scientific applications involve operations on large sparse matrices such as linear solvers, eigensolver, and graph mining algorithms. The core of most of these applications involves the multiplication of a large, sparse matrix with a dense vector (SpMV). In this paper, we investigate the performance of the Xeon Phi coprocessor for SpMV. We first provide a comprehensive introduction to this new architecture and analyze its peak performance with a number of micro benchmarks. Although the design of a Xeon Phi core is not much different than those of the cores in modern processors, its large number of cores and hyperthreading capability allow many application to saturate the available memory bandwidth, which is not the case for many cutting-edge processors. Yet, our performance studies show that it is the memory latency not the bandwidth which creates a bottleneck for SpMV on this architecture. Finally, our experiments show that Xeon Phi's sparse kernel performance is very promising and even better than that of cutting-edge general purpose processors and GPUs

A Review of Lightweight Thread Approaches for High Performance Computing

High-level, directive-based solutions are becoming the programming models (PMs) of the multi/many-core architectures. Several solutions relying on operating system (OS) threads perfectly work with a moderate number of cores. However, exascale systems will spawn hundreds of thousands of threads in order to exploit their massive parallel architectures and thus conventional OS threads are too heavy for that purpose. Several lightweight thread (LWT) libraries have recently appeared offering lighter mechanisms to tackle massive concurrency. In order to examine the suitability of LWTs in high-level runtimes, we develop a set of microbenchmarks consisting of commonly-found patterns in current parallel codes. Moreover, we study the semantics offered by some LWT libraries in order to expose the similarities between different LWT application programming interfaces. This study reveals that a reduced set of LWT functions can be sufficient to cover the common parallel code patterns andthat those LWT libraries perform better than OS threads-based solutions in cases where task and nested parallelism are becoming more popular with new architectures.The researchers from the Universitat Jaume I de Castelló were supported by project TIN2014-53495-R of the MINECO, the Generalitat Valenciana fellowship programme Vali+d 2015, and FEDER. This work was partially supported by the U.S. Dept. of Energy, Office of Science, Office of Advanced Scientific Computing Research (SC-21), under contract DEAC02-06CH11357. We gratefully acknowledge the computing resources provided and operated by the Joint Laboratory for System Evaluation (JLSE) at Argonne National Laboratory.Peer ReviewedPostprint (author's final draft

Configurable Strategies for Work-stealing

Work-stealing systems are typically oblivious to the nature of the tasks they are scheduling. For instance, they do not know or take into account how long a task will take to execute or how many subtasks it will spawn. Moreover, the actual task execution order is typically determined by the underlying task storage data structure, and cannot be changed. There are thus possibilities for optimizing task parallel executions by providing information on specific tasks and their preferred execution order to the scheduling system. We introduce scheduling strategies to enable applications to dynamically provide hints to the task-scheduling system on the nature of specific tasks. Scheduling strategies can be used to independently control both local task execution order as well as steal order. In contrast to conventional scheduling policies that are normally global in scope, strategies allow the scheduler to apply optimizations on individual tasks. This flexibility greatly improves composability as it allows the scheduler to apply different, specific scheduling choices for different parts of applications simultaneously. We present a number of benchmarks that highlight diverse, beneficial effects that can be achieved with scheduling strategies. Some benchmarks (branch-and-bound, single-source shortest path) show that prioritization of tasks can reduce the total amount of work compared to standard work-stealing execution order. For other benchmarks (triangle strip generation) qualitatively better results can be achieved in shorter time. Other optimizations, such as dynamic merging of tasks or stealing of half the work, instead of half the tasks, are also shown to improve performance. Composability is demonstrated by examples that combine different strategies, both within the same kernel (prefix sum) as well as when scheduling multiple kernels (prefix sum and unbalanced tree search)

Real-Time Twitter Recommendation: Online Motif Detection in Large Dynamic Graphs

We describe a production Twitter system for generating relevant, personalized, and timely recommendations based on observing the temporally-correlated actions of each user’s followings. The system currently serves millions of recommendations daily to tens of millions of mobile users. The approach can be viewed as a specific instance of the novel problem of online motif detection in large dynamic graphs. Our current solution partitions the graph across a number of machines, and with the construction of appropriate data structures, motif detection can be translated into the lookup and intersection of adjacency lists in each partition. We conclude by discussing a generalization of the problem that perhaps represents a new class of data management systems. 1

Streaming Breakpoint Graph Analytics for Accelerating and Parallelizing the Computation of DCJ Median of Three Genomes

AbstractThe problem of finding the median of three genomes is the key process in building the most parsimonious phylogenetic trees from genome rearrangement data. The median problem using Double-Cut-and-Join (DCJ) distance is NP-hard and the best exact algorithm is based on a branch-and-bound best-first search strategy to explore sub-graph patterns in Multiple BreakPoint Graph (MBG). In this paper, by taking advantage of the “streaming” property of MBG, we introduce the “footprint-based” data structure to reduce the space requirement of a single search nodes from O(v2) to O(v); minimize the redundant computation in counting cycles/paths to update bounds, which leads to dramatically decrease of workload of a single search node. Additional heuristic of branching strategy is introduced to help reducing the searching space. Last but not least, the introduction of a multi-thread shared memory parallel algorithm with two load balancing strategies bring in additional benefit by distributing search work efficiently among different processors. We conduct extensive experiments on simulated datasets and our results show significant improvement on all datasets. And we test our DCJ median algorithm with GASTS, a state of the art software phylogenetic tree construction package. On the real high resolution Drosophila data set, our exact algorithm run as fast as the heuristic algorithm and help construct a better phylogenetic tree

Incremental closeness centrality in distributed memory

Networks are commonly used to model traffic patterns, social interactions, or web pages. The vertices in a network do not possess the same characteristics: some vertices are naturally more connected and some vertices can be more important. Closeness centrality (CC) is a global metric that quantifies how important is a given vertex in the network. When the network is dynamic and keeps changing, the relative importance of the vertices also changes. The best known algorithm to compute the CC scores makes it impractical to recompute them from scratch after each modification. In this paper, we propose Streamer, a distributed memory framework for incrementally maintaining the closeness centrality scores of a network upon changes. It leverages pipelined, replicated parallelism, and SpMM-based BFSs, and it takes NUMA effects into account. It makes maintaining the Closeness Centrality values of real-life networks with millions of interactions significantly faster and obtains almost linear speedups on a 64 nodes 8 threads/node cluster

GLT: A Unified API for Lightweight Thread Libraries

In recent years, several lightweight thread (LWT) libraries have emerged to tackle exascale challenges. These offer programming models (PMs) based on user-level threads and incorporate their own lightweight mechanisms. However, each library proposes its own PM, exposing different semantics and hindering portability. To address this drawback, we have designed Generic Lightweight Thread (GLT), an application programming interface that frames the functionality of the most popular LWT libraries for high-performance computing under a single PM. We implement GLT on top of Argobots, MassiveThreads, and Qthreads. We provide GLT as a dynamic library, as well as in the form of a static version based on macro preprocessing resolution to reduce overhead. This paper discusses the GLT PM and demonstrates its minimal performance impact.Researchers from the Universitat Jaume I de Castelló were supported by project TIN2014-53495-R of the MINECO, the Generalitat Valenciana fellowship programme Vali+d 2015, and FEDER. Antonio J. Peña is cofinancied by the Spanish Ministry of Economy and Competitiveness under Juan de la Cierva fellowship number IJCI-2015-23266. This work was partially supported by the U.S. Dept. of Energy, Office of Science, Office of Advanced Scientific Computing Research (SC-21), under contract DE-AC02-06CH11357.Peer ReviewedPostprint (author's final draft