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Parallel Tree Accumulations on MapReduce

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Abstract

MapReduce is a remarkable parallel programming model as well as a parallel processing infrastructure for large-scale data processing. Since it is now widely available on cloud environments, developing methodology or patterns for MapReduce programming is important. In particular, XML is the de facto standard for representing data, and processing semi-structured data is involved in many applications. The target computational patterns in this paper are tree accumulations. Tree accumulations are shape-preserving computations over a tree in which values are updated through flows over the tree. We develop BSP algorithms for two tree accumulations as extensions of the BSP algorithm for tree reduction by Kakehi et al. (Tech. Rep. METR 2006-64, Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 2006). We also implemented the two-superstep algorithms with a single MapReduce execution. Experimental results on a 16-node PC cluster show good speedups of a factor of 10.9–12.7.

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Notes

  1. In Haskell, we need sectioning to handle operators as functions, e.g., \((\oplus )\). In this paper, we simply write operators without sectioning when used as function parameters.

  2. Since it is allowed for \(f_\mathrm{reduce}\) to output no result, the result type of \(f_\mathrm{reduce}\) is specified by a maybe type.

  3. In the functional programming community, the tree of the type \(\textit{Tree}~\alpha \) is called a rose tree [20].

  4. If some other properties hold on the parameter operators \(\oplus \) and \(\otimes \), we may be able to extract more parallelism. We can find discussions of such a property in [15, 19]. Note that we only require the associativity of \(\otimes \) in this paper.

  5. This definition is slightly different from that in the original paper [15]. Our \(\textit{as}\) corresponds to their \(\textit{cs}\), and our \(\textit{ds}\) corresponds to two lists \(\textit{as}\) and \(\textit{bs}\) in their definition.

    Fig. 5
    figure 5

    Local computation of tree reduction that returns hNF. Tree reduction is applied to the nodes in dashed lines

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Acknowledgments

This work was conducted in the PaPDAS project supported by ANR (ANR-2010-INTB-0205-02) and JST (10102704).

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  1. School of Information, Kochi University of Technology, 185 Tosayamadacho-Miyanokuchi, Kami, Kochi, Japan

    Kiminori Matsuzaki & Reina Miyazaki

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  1. Kiminori Matsuzaki
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  2. Reina Miyazaki
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Correspondence to Kiminori Matsuzaki.

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Matsuzaki, K., Miyazaki, R. Parallel Tree Accumulations on MapReduce. Int J Parallel Prog 44, 466–485 (2016). https://doi.org/10.1007/s10766-015-0355-8

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