Fast PageRank Computation via a Sparse Linear System

Recently, the research community has devoted increased attention to reducing the computational time needed by web ranking algorithms. In particular, many techniques have been proposed to speed up the well-known PageRank algorithm used by Google. This interest is motivated by two dominant factors: (1) the web graph has huge dimensions and is subject to dramatic updates in terms of nodes and links, therefore the PageRank assignment tends to became obsolete very soon; (2) many PageRank vectors need to be computed according to different choices of the personalization vectors or when adopting strategies of collusion detection. In this paper, we show how the PageRank computation in the original random surfer model can be transformed in the problem of computing the solution of a sparse linear system. The sparsity of the obtained linear system makes it possible to exploit the effectiveness of the Markov chain index reordering to speed up the PageRank computation. In particular, we rearrange the system matrix according to several permutations, and we apply different scalar and block iterative methods to solve smaller linear systems. We tested our approaches on web graphs crawled from the net. The largest one contains about 24 millions nodes and more than 100 million links. Upon this web graph, the cost for computing the PageRank is reduced by 65% in terms of Mflops and by 92% in terms of time respect to the power method commonly used.