A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations

Abstract

We address the PageRank problem of associating a relative importance value to all web pages in the Internet so that a search engine can use them to sort which pages to show to the user. This precludes finding the eigenvector associated with a particular eigenvalue of the link matrix constructed from the topology graph of the web. In this paper, we investigate the potential benefits of addressing the problem as a solution of a set of linear equations. Initial results suggest that using an asynchronous version of the Gauss-Seidel method can yield a faster convergence than using the traditional power method while maintaining the communications according to the sparse link matrix of the web and avoiding the strict sequential update of the Gauss-Seidel method. Such an alternative poses an interesting path for future research given the benefits of using other more advanced methods to solve systems of linear equations. Additionally, it is investigated the benefits of having a projection after all page ranks have been updated as to maintain all its entries summing to one and positive. In simulations, it is provided evidence to support future research on approximation rules that can be used to avoid the need for the projection to the $n$-simplex (the projection represents in some cases a threefold increase in the convergence rate over the power method) and on the loss in performance by using an asynchronous algorithm.