12,391 research outputs found

    Scalable Parallel Algorithms for Massive Scale-free Graphs

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    Efficiently storing and processing massive graph data sets is a challenging problem as researchers seek to leverage “Big Data” to answer next-generation scientific questions. New techniques are required to process large scale-free graphs in shared, distributed, and external memory. This dissertation develops new techniques to parallelize the storage, computation, and communication for scale-free graphs with high-degree vertices. Our work facilitates the processing of large real-world graph datasets through the development of parallel algorithms and tools that scale to large computational and memory resources, overcoming challenges not addressed by existing techniques. Our aim is to scale to trillions of edges, and our research is targeted at leadership class supercomputers, clusters with local non-volatile memory, and shared memory systems. We present three novel techniques to address scaling challenges in processing large scale-free graphs. We apply an asynchronous graph traversal technique using prioritized visitor queues that is capable of tolerating data latencies to the external graph storage media and message passing communication. To accommodate large high-degree vertices, we present an edge list partitioning technique that evenly partitions graphs containing high-degree vertices. Finally, we propose a technique we call distributed delegates that distributes and parallelizes the storage, computation, and communication when processing high-degree vertices. The edges of high-degree vertices are distributed, providing additional opportunities for parallelism not present in existing methods. We apply our techniques to multiple graph algorithms: Breadth-First Search, Single Source Shortest Path, Connected Components, K-Core decomposition, Triangle Counting, and Page Rank. Our experimental study of these algorithms demonstrates excellent scalability on supercomputers, clusters with non-volatile memory, and shared memory systems. Our study includes multiple synthetic scale-free graph models, the largest of which has trillion edges, and real-world input graphs. On a supercomputer, we demonstrate scalability up to 131K processors, and improve the best known Graph500 results for IBM BG/P Intrepid by 15%

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

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    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

    On Large-Scale Graph Generation with Validation of Diverse Triangle Statistics at Edges and Vertices

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    Researchers developing implementations of distributed graph analytic algorithms require graph generators that yield graphs sharing the challenging characteristics of real-world graphs (small-world, scale-free, heavy-tailed degree distribution) with efficiently calculable ground-truth solutions to the desired output. Reproducibility for current generators used in benchmarking are somewhat lacking in this respect due to their randomness: the output of a desired graph analytic can only be compared to expected values and not exact ground truth. Nonstochastic Kronecker product graphs meet these design criteria for several graph analytics. Here we show that many flavors of triangle participation can be cheaply calculated while generating a Kronecker product graph. Given two medium-sized scale-free graphs with adjacency matrices AA and BB, their Kronecker product graph has adjacency matrix C=ABC = A \otimes B. Such graphs are highly compressible: E|{\cal E}| edges are represented in O(E1/2){\cal O}(|{\cal E}|^{1/2}) memory and can be built in a distributed setting from small data structures, making them easy to share in compressed form. Many interesting graph calculations have worst-case complexity bounds O(Ep){\cal O}(|{\cal E}|^p) and often these are reduced to O(Ep/2){\cal O}(|{\cal E}|^{p/2}) for Kronecker product graphs, when a Kronecker formula can be derived yielding the sought calculation on CC in terms of related calculations on AA and BB. We focus on deriving formulas for triangle participation at vertices, tC{\bf t}_C, a vector storing the number of triangles that every vertex is involved in, and triangle participation at edges, ΔC\Delta_C, a sparse matrix storing the number of triangles at every edge.Comment: 10 pages, 7 figures, IEEE IPDPS Graph Algorithms Building Block

    Gunrock: GPU Graph Analytics

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    For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs, have presented two significant challenges to developing a programmable high-performance graph library. "Gunrock", our graph-processing system designed specifically for the GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high performance GPU computing primitives and optimization strategies with a high-level programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. We characterize the performance of various optimization strategies and evaluate Gunrock's overall performance on different GPU architectures on a wide range of graph primitives that span from traversal-based algorithms and ranking algorithms, to triangle counting and bipartite-graph-based algorithms. The results show that on a single GPU, Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives and CPU shared-memory graph libraries such as Ligra and Galois, and better performance than any other GPU high-level graph library.Comment: 52 pages, invited paper to ACM Transactions on Parallel Computing (TOPC), an extended version of PPoPP'16 paper "Gunrock: A High-Performance Graph Processing Library on the GPU

    Comparing MapReduce and pipeline implementations for counting triangles

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    A generalized method to define the Divide & Conquer paradigm in order to have processors acting on its own data and scheduled in a parallel fashion. MapReduce is a programming model that follows this paradigm, and allows for the definition of efficient solutions by both decomposing a problem into steps on subsets of the input data and combining the results of each step to produce final results. Albeit used for the implementation of a wide variety of computational problems, MapReduce performance can be negatively affected whenever the replication factor grows or the size of the input is larger than the resources available at each processor. In this paper we show an alternative approach to implement the Divide & Conquer paradigm, named pipeline. The main features of pipeline are illustrated on a parallel implementation of the well-known problem of counting triangles in a graph. This problem is especially interesting either when the input graph does not fit in memory or is dynamically generated. To evaluate the properties of pipeline, a dynamic pipeline of processes and an ad-hoc version of MapReduce are implemented in the language Go, exploiting its ability to deal with channels and spawned processes. An empirical evaluation is conducted on graphs of different sizes and densities. Observed results suggest that pipeline allows for the implementation of an efficient solution of the problem of counting triangles in a graph, particularly, in dense and large graphs, drastically reducing the execution time with respect to the MapReduce implementation.Peer ReviewedPostprint (published version

    Comparing MapReduce and pipeline implementations for counting triangles

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    A common method to define a parallel solution for a computational problem consists in finding a way to use the Divide and Conquer paradigm in order to have processors acting on its own data and scheduled in a parallel fashion. MapReduce is a programming model that follows this paradigm, and allows for the definition of efficient solutions by both decomposing a problem into steps on subsets of the input data and combining the results of each step to produce final results. Albeit used for the implementation of a wide variety of computational problems, MapReduce performance can be negatively affected whenever the replication factor grows or the size of the input is larger than the resources available at each processor. In this paper we show an alternative approach to implement the Divide and Conquer paradigm, named dynamic pipeline. The main features of dynamic pipelines are illustrated on a parallel implementation of the well-known problem of counting triangles in a graph. This problem is especially interesting either when the input graph does not fit in memory or is dynamically generated. To evaluate the properties of pipeline, a dynamic pipeline of processes and an ad-hoc version of MapReduce are implemented in the language Go, exploiting its ability to deal with channels and spawned processes. An empirical evaluation is conducted on graphs of different topologies, sizes, and densities. Observed results suggest that dynamic pipelines allows for an efficient implementation of the problem of counting triangles in a graph, particularly, in dense and large graphs, drastically reducing the execution time with respect to the MapReduce implementation.Peer ReviewedPostprint (published version

    Dynamic Graphs on the GPU

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    We present a fast dynamic graph data structure for the GPU. Our dynamic graph structure uses one hash table per vertex to store adjacency lists and achieves 3.4–14.8x faster insertion rates over the state of the art across a diverse set of large datasets, as well as deletion speedups up to 7.8x. The data structure supports queries and dynamic updates through both edge and vertex insertion and deletion. In addition, we define a comprehensive evaluation strategy based on operations, workloads, and applications that we believe better characterize and evaluate dynamic graph data structures
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