  Over the last decade, PageRank has gained importance in a wide range of
applications and domains, ever since it first proved to be effective in
determining node importance in large graphs (and was a pioneering idea behind
Google's search engine). In distributed computing alone, PageRank vector, or
more generally random walk based quantities have been used for several
different applications ranging from determining important nodes, load
balancing, search, and identifying connectivity structures. Surprisingly,
however, there has been little work towards designing provably efficient
fully-distributed algorithms for computing PageRank. The difficulty is that
traditional matrix-vector multiplication style iterative methods may not always
adapt well to the distributed setting owing to communication bandwidth
restrictions and convergence rates.
  In this paper, we present fast random walk-based distributed algorithms for
computing PageRanks in general graphs and prove strong bounds on the round
complexity. We first present a distributed algorithm that takes $O\big(\log
n/\eps \big)$ rounds with high probability on any graph (directed or
undirected), where $n$ is the network size and $\eps$ is the reset probability
used in the PageRank computation (typically $\eps$ is a fixed constant). We
then present a faster algorithm that takes $O\big(\sqrt{\log n}/\eps \big)$
rounds in undirected graphs. Both of the above algorithms are scalable, as each
node sends only small ($\polylog n$) number of bits over each edge per round.
To the best of our knowledge, these are the first fully distributed algorithms
for computing PageRank vector with provably efficient running time.
