Fast Incremental and Personalized PageRank

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In this paper, we analyze the efficiency of Monte Carlo methods for incremental computation of PageRank, personalized PageRank, and similar random walk based methods (with focus on SALSA), on large-scale dynamically evolving social networks.

• We assume that the graph of friendships is stored in distributed shared memory, as is the case for large social networks such as Twitter.
• For global PageRank, we assume that the social network has $n$ nodes, and $m$ adversarially chosen edges arrive in a random order.
• We show that with a reset probability of $\epsilon$, the total work needed to maintain an accurate estimate (using the Monte Carlo method) of the PageRank of every node at all times is $O(\frac{n\ln m}{\epsilon^{2}})$.