## Improved Communication Cost in Distributed PageRank Computation – A Theoretical Study

### Siqiang Luo

Keywords: [ Computational Learning Theory ] [ Information Theory and Estimation ] [ Learning Theory ]

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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 $O(\frac{1}{\log^d{n}})$ under a generalized congested clique distributed 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 the worst case. 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.