  Personalized PageRank (PPR) has enormous applications, such as link
prediction and recommendation systems for social networks, which often require
the fully PPR to be known. Besides, most of real-life graphs are edge-weighted,
e.g., the interaction between users on the Facebook network. However, it is
computationally difficult to compute the fully PPR, especially on large graphs,
not to mention that most existing approaches do not consider the weights of
edges. In particular, the existing approach cannot handle graphs with billion
edges on a moderate-size cluster. To address this problem, this paper presents
a novel study on the computation of fully edge-weighted PPR on large graphs
using the distributed computing framework. Specifically, we employ the Monte
Carlo approximation that performs a large number of random walks from each node
of the graph, and exploits the parallel pipeline framework to reduce the
overall running time of the fully PPR. Based on that, we develop several
optimization techniques which (i) alleviate the issue of large nodes that could
explode the memory space, (ii) pre-compute short walks for small nodes that
largely speedup the computation of random walks, and (iii) optimize the amount
of random walks to compute in each pipeline that significantly reduces the
overhead. With extensive experiments on a variety of real-life graph datasets,
we demonstrate that our solution is several orders of magnitude faster than the
state-of-the-arts, and meanwhile, largely outperforms the baseline algorithms
in terms of accuracy.
