Improved Communication Cost in Distributed PageRank Computation – A Theoretical Study
Abstract
PageRank is a widely used approach for measuring the importance of a node in a graph. Due to the rapid growth of the graph size in the real world, the importance of computing PageRanks in a distributed environment has been increasingly recognized. However, only a few previous works can provide a provable complexity and accuracy for distributed PageRank computation. Given a constant $d\ge 1$ and a graph of $n$ nodes, the state-of-the-art approach, Radar-Push, uses $O(\log\log{n}+\log{d})$ communication rounds to approximate the PageRanks within a relative error $\Theta(\frac{1}{\log^d{n}})$ under a generalized congested clique distributed computation model. However, Radar-Push entails as large as $O(\log^{2d+3}{n})$ bits of bandwidth (e.g., the communication cost between a pair of nodes per round). In this paper, we provide a new algorithm that uses asymptotically the same communication round complexity while using only $O(d\log^3{n})$ bits of bandwidth.
BibTeX
@InProceedings{pmlr-v119-luo20a,
title = {Improved Communication Cost in Distributed {P}age{R}ank Computation {–} A Theoretical Study},
author = {Luo, Siqiang},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {6459--6467},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/luo20a/luo20a.pdf},
url = {https://proceedings.mlr.press/v119/luo20a.html},
abstract = {PageRank is a widely used approach for measuring the importance of a node in a graph. Due to the rapid growth of the graph size in the real world, the importance of computing PageRanks in a distributed environment has been increasingly recognized. However, only a few previous works can provide a provable complexity and accuracy for distributed PageRank computation. Given a constant $d\ge 1$ and a graph of $n$ nodes, the state-of-the-art approach, Radar-Push, uses $O(\log\log{n}+\log{d})$ communication rounds to approximate the PageRanks within a relative error $\Theta(\frac{1}{\log^d{n}})$ under a generalized congested clique distributed computation model. However, Radar-Push entails as large as $O(\log^{2d+3}{n})$ bits of bandwidth (e.g., the communication cost between a pair of nodes per round). In this paper, we provide a new algorithm that uses asymptotically the same communication round complexity while using only $O(d\log^3{n})$ bits of bandwidth.}
}