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Flexible partitioning for selective binary theta-joins in a massively parallel setting

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Abstract

Efficient join processing plays an important role in big data analysis. In this work, we focus on generic theta joins in a massively parallel environment, such as MapReduce and Spark. Theta joins are notoriously slow due to their inherent quadratic complexity, even when their selectivity is low, e.g., 1%. The main performance bottleneck differs between cases, and is due to any of the following factors or their combination: amount of data being shuffled, memory load on reducers, or computation load on reducers. We propose an ensemble-based partitioning approach that tackles all three aspects. In this way, we can save communication cost, we better respect the memory and computation limitations of reducers and overall, we reduce the total execution time. The key idea behind our partitioning is to cluster join key values following two techniques, namely matrix re-arrangement and agglomerative clustering. These techniques can run either in isolation or in combination. We present thorough experimental results using both band queries on real data and arbitrary synthetic predicates. We show that we can save up to 45% of the communication cost and reduce the computation load of a single reducer up to 50% in band queries, whereas the savings are up to 74 and 80%, respectively, in queries with arbitrary theta predicates. Apart from being effective, the potential benefits of our approach can be estimated before execution from metadata, which allows for informed partitioning decisions. Finally, our solutions are flexible in that they can account for any weighted combination of the three bottleneck factors.

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Notes

  1. In our 4-page abstract [16], we provide a preliminary version of the material in Sect. 4. All the remainder material in this work is novel.

  2. In the remainder of this work we will use the terms region, partition and group interchangeably; we will also use the term reducer for the worker node, where local join processing takes place, but this does not imply that we are tailored to a MapReduce setting only.

  3. It is also trivial to express imb as a function of mri and rep through simple algebraic manipulation.

  4. http://www.math.uwaterloo.ca/tsp/concorde/.

  5. TSPk is implemented according to [9], the code of which has been integrated into our codebase under the https://github.com/JohnKoumarelas/binarythetajoins/tree/master/btj/tspk directory.

  6. Available from http://cdiac.ornl.gov/ftp/ndp026c/.

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Acknowledgements

We would like to thank Jordi Torres, Rubèn Tous and Carlos Tripiana from the Barcelona Supercomputing Center for their help in running the Spark experiments.

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Authors and Affiliations

  1. Department of Informatics, Hasso-Plattner-Institut, Potsdam, Germany

    Ioannis Koumarelas

  2. Department of Informatics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Athanasios Naskos & Anastasios Gounaris

Authors
  1. Ioannis Koumarelas
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  2. Athanasios Naskos
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  3. Anastasios Gounaris
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Corresponding author

Correspondence to Anastasios Gounaris.

Appendix: Additional evaluation results

Appendix: Additional evaluation results

Table 7 Summary improvements due to the re-arrangement policies grouped by the number of reducers (for band queries)
Full size table
Table 8 Summary improvements due to the re-arrangement policies grouped by the number of bands (for band queries)
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Table 9 Summary improvements due to the re-arrangement policies grouped by the number of reducers (for band queries)
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Table 10 Summary improvements due to the re-arrangement policies grouped by the number of reducers (for random queries)
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Tables 7 and 8 refer to the experiments in Sect. 6.3 for the band queries on solar altitude. Table 8 presents the same results as Table 7 but groups the experiments differently to show the impact of selectivity (in terms of number of bands). Although the behavior differs according to the number of bands, the impact of selectivity is considered to be small. The second column (coverage) shows the percentage of the cases, where an improvement on M-Bucket-I is achieved by any technique, i.e., it answers the question “How frequently matrix re-arrangement leads to improvements?”, whereas the other columns answer the question “How high are the improvements when they happen?”. Further observations that can be drawn are: (i) The higher the number of reducers, the less frequently matrix re-arrangement yields improvements. (ii) The benefits on OF values due to the re-arrangement techniques may come at the expense of a small degradation of imbalance, as shown in the last column, but in general imb is not affected much. (iii) There are several cases where the improvement is very small or negligible. Table 9 shows the corresponding details for the band queries on longitude, where the best improvements on mrcl are up to 44%. Table 10 shows the impact of the re-arrangement techniques on the OFs for random queries with \(100 \times 100\) JM. The main observation is that, compared to Table 7, both the coverage and the improvements are higher; e.g., we have observed reductions in rep by 74% (i.e., nearly 4 times less) and in mrcl by 56%. For random queries with \(200 \times 200\) JMs, the improvements are of lower magnitude but the coverage is 88% (no detailed results are presented).

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Koumarelas, I., Naskos, A. & Gounaris, A. Flexible partitioning for selective binary theta-joins in a massively parallel setting. Distrib Parallel Databases 36, 301–337 (2018). https://doi.org/10.1007/s10619-017-7214-0

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