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Algorithms and framework for computing 2-body statistics on GPUs

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Abstract

Various types of two-body statistics (2-BS) are regarded as essential components of low-level data analysis in scientific database systems. In relational algebraic terms, a 2-BS is essentially a Cartesian product between two datasets (or two instances of the same dataset) followed by a user-defined aggregate. The quadratic complexity of these computations hinders timely processing of data. Use of modern parallel hardware has thus become an obvious solution to meet such challenges. This paper presents our recent work on designing and optimizing parallel algorithms for 2-BS computation on Graphics Processing Units (GPUs). Although a typical 2-BS problem can be summarized into a straightforward parallel computing pattern, traditional knowledge from (general) parallel computing often falls short in delivering the best possible performance. Therefore, we present a suite of techniques to decompose 2-BS problems and methods for effective use of computing resources on GPUs. We also develop analytical models that guide us towards finding the best parameters of our GPU programs. As a result, we achieve the design of highly-optimized 2-BS algorithms that significantly outperform the best known GPU and CPU implementations. Although 2-BS problems share the same core computations, each 2-BS problem however carries its own characteristics that calls for different strategies in code optimization. For that, we develop a software framework that automatically generates high-performance GPU code based on a few parameters and short primer code input. We further present two case studies to demonstrate that code generated by this framework reaches a very high level of efficiency.

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Notes

  1. We focus our discussions on 2-BSs defined over a single dataset with commutative distance function (i.e., only one function call is needed for every pair of points). Therefore, the point with index i is only paired with all data points beyond position i. Note there are cases where 2-BS is defined between two different datasets (e.g., relational join) or with non-commutative distance function (e.g., SVM kernel functions). We will mention them in coming sections as needed.

  2. The NVlink bus found in newer GPUs provides a higher bandwidth but does not fundamentally change the fact that data transmission is the bottleneck.

  3. It is easy to find a block size to satisfy this condition due to the quadratic computational time.

  4. We also run experiments on skewed datasets. However, the performance of 2-BS algorithms is not affected by data distribution thus we omit those results.

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Acknowledgements

This work is supported by an award (IIS-1253980) from the National Science Foundation (NSF) of U.S.A.. Equipments used in the experiments are partially supported by another grant (CNS-1513126) from the same agency.

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  1. Department of Computer Science and Engineering, University of South Florida, 4202 E. Fowler Ave., ENB118, Tampa, FL, 33613, USA

    Napath Pitaksirianan, Zhila Nouri Lewis & Yi-Cheng Tu

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  1. Napath Pitaksirianan
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Correspondence to Napath Pitaksirianan.

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Pitaksirianan, N., Lewis, Z.N. & Tu, YC. Algorithms and framework for computing 2-body statistics on GPUs. Distrib Parallel Databases 37, 587–622 (2019). https://doi.org/10.1007/s10619-018-7238-0

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