Accelerated Evolving Set Processes for Local PageRank Computation

This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified linear system. We show that the time complexity of such localized methods is upper bounded by min{ O(R2/ϵ2), O(m)}to obtain an ϵ-approximation of the PPR vector, where m denotes the number of edges in the graph and R is a constant defined via nested evolving set processes. Furthermore, the algorithms induced by our framework require solving only O(1/ α) such linear systems, where α is the damping factor. When 1/ϵ2 m, this implies the existence of an algorithm that computes an ϵ-approximation of the PPR vector with an overall time complexity of O(R2/( αϵ2)), independent of the underlying graph size.