Fast PageRank Computation Via a Sparse Linear System (Extended Abstract)

The research community has devoted an increased attention to reduce the computation time needed by Web ranking algorithms. Many efforts have been devoted to improve PageRank [4, 23], the well known ranking algorithm used by Google. The core of PageRank exploits an iterative weight assignment of ranks to the Web pages, until a fixed point is reached. This fixed point turns out to be the (dominant) eigenpair of a matrix derived by the Web Graph itself. Brin and Page originally suggested to compute this pair using the well-known Power method [12] and they also gave a nice interpretation of PageRank in terms of Markov Chains. Recent studies about PageRank address at least two different needs. First, the desire to reduce the time spent weighting the nodes of the Web Graph which takes several days. Second, to assign many PageRank values to each Web page, as results of PageRank’s personalization [14–16] that was recently presented by Google as beta-service (see http://labs.google.com/personalized/). The Web changes very rapidly and more than 25% of links are changed and 5% of ”new content” is created in a week [8]. This result indicates that search engines need to update link based ranking metrics (such as PageRank) very often and that a week-old ranking may not reflect very well the current importance of the pages. This motivates the need of accelerating the PageRank computation. Previous approaches followed different directions such as the attempt to compress the Web Graph to fit it into main memory [3], or the implementation in external memory of the algorithms [13, 7]. The very interesting research track exploits efficient numerical methods to reduce the computation time. These kind of numerical techniques are the most promising and we have seen many intriguing results in the last few years to accelerate the convergence of Power iterations [18, 13, 21]. In the literature [1, 21, 23] are presented models which treat in a different way pages with no out-links. In this paper we consider the original PageRank model (see Section 2) and, by using numerical techniques, we show that this problem can be transformed in an equivalent linear system of equations, where the coefficient matrix is as sparse as the Web Graph itself. This new formulation of the