Exploiting Web matrix permutations to speedup PageRank computation
Gianna M. Del Corso, Antonio Gullì, Francesco Romani · 2004
Recently, the research community has devoted an increased attention to reduce the computational time needed by Web ranking algorithms. In particular, we saw many proposals 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 it is subject to dramatic updates in term of nodes and links - therefore PageRank assignment tends to became obsolete very soon; (2) many PageRank vectors need to be computed according to di#erent personalization vectors chosen. In the present paper, we address this problem from a numerical point of view. First, we show how to treat dangling nodes in a way which naturally adapts to the random surfer model and preserves the sparsity of the Web Graph. This result allows to consider the PageRank computation as a sparse linear system in alternative to the commonly adopted eigenpairs interpretation. Second, we exploit the Web Matrix reducibility and compose opportunely some Web matrix permutation to speed up the PageRank computation. We tested our approaches on a Web Graphs crawled from the net. The largest one account about 24 millions nodes and more than 100 million links. Upon this Web Graph, the cost for computing the PageRank is reduced of 58% in terms of Mflops and of 89% in terms of time respect to the Power method commonly used.