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Efficient distributed algorithms for holistic aggregation functions on random regular graphs

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Abstract

In this paper, we propose efficient distributed algorithms for three holistic aggregation functions on random regular graphs that are good candidates for network topology in next-generation data centers. The three holistic aggregation functions include SELECTION (select the k-th largest or smallest element), DISTINCT (query the count of distinct elements), MODE (query the most frequent element). We design three basic techniques — Pre-order Network Partition, Pairwise-independent Random Walk, and Random Permutation Delivery, and devise the algorithms based on the techniques. The round complexity of the distributed SELECTION is Θ(log N) which meets the lower bound where N is the number of nodes and each node holds a numeric element. The round complexity of the distributed DISTINCT and MODE algorithms are O(log3N / log log N) and O(log2N log log N) respectively. All of our results break the lower bounds obtained on general graphs and our distributed algorithms are all based on the \({\cal C}{\cal O}{\cal N}{\cal G}{\cal E}{\cal S}{\cal T}\) model, which restricts each node to send only O(log N) bits on each edge in one round under synchronous communications.

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61972447, 61832006) and the Fundamental Research Funds for the Central Universities (Grant No. 2019kfyXKJC021). We thank the anonymous reviewers for the helpful comments to improve the presentation of this paper.

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Authors and Affiliations

  1. National Engineering Research Center for Big Data Technology and System/Services Computing Technology and System Lab/Cluster and Grid Computing Lab, School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Lin Jia, Qiang-Sheng Hua, Qiuping Wang & Hai Jin

  2. Institute for Interdisciplinary Information Science, Tsinghua University, Beijing, 100084, China

    Haoqiang Fan

Authors
  1. Lin Jia
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  2. Qiang-Sheng Hua
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  3. Haoqiang Fan
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  4. Qiuping Wang
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  5. Hai Jin
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Correspondence to Qiang-Sheng Hua.

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Jia, L., Hua, QS., Fan, H. et al. Efficient distributed algorithms for holistic aggregation functions on random regular graphs. Sci. China Inf. Sci. 65, 152101 (2022). https://doi.org/10.1007/s11432-020-2996-2

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