Zoltan2 for Extreme-Scale Data Partitioning: Sampling and Partitioning
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2014 IEEE High Performance Extreme Computing Conference, HPEC 2014
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. These problems become more difficult as the background graph grows larger and noisier and the coordination patterns become more subtle. In this paper, we discuss the computational challenges of a statistical framework designed to address this cross-mission challenge. The statistical framework is based on spectral analysis of the graph data, and three partitioning methods are evaluated for computing the principal eigenvector of the graph's residuals matrix. While a standard one-dimensional partitioning technique enables this computation for up to four billion vertices, the communication overhead prevents this method from being used for even larger graphs. Recent two-dimensional partitioning methods are shown to have much more favorable scaling properties. A data-dependent partitioning method, which has the best scaling performance, is also shown to improve computation time even as a graph changes over time, allowing amortization of the upfront cost.
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The outline of this presentation is: (1) High-level view of Zoltan; (2) Requirements, data models, and interface; (3) Load Balancing and Partitioning; (4) Matrix Ordering, Graph Coloring; (5) Utilities; (6) Isorropia; and (7) Zoltan2.
The objectives of this presentation are: (1) Learn how to partition a problem using Zoltan; (2) Understand the following (a) Basic process of partitioning with Zoltan, (b) Setting Zoltan parameters, (c) Registering query functions, (d) Writing query functions, (e) Zoltan-LB-Partition and its input/output; and (3) Be able to integrate Zoltan into your own applications.
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As computational science applications grow more parallel with multi-core supercomputers having hundreds of thousands of computational cores, it will become increasingly difficult for solvers to scale. Our approach is to use hybrid MPI/threaded numerical algorithms to solve these systems in order to reduce the number of MPI tasks and increase the parallel efficiency of the algorithm. However, we need efficient threaded numerical kernels to run on the multi-core nodes in order to achieve good parallel efficiency. In this paper, we focus on improving the performance of a multithreaded triangular solver, an important kernel for preconditioning. We analyze three factors that affect the parallel performance of this threaded kernel and obtain good scalability on the multi-core nodes for a range of matrix sizes.
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