Personalized PageRank to a Target Node

TL;DR

This paper introduces an efficient algorithm for computing personalized PageRank scores to a specific target node from all source nodes, significantly improving speed over previous methods and demonstrated with Twitter graph experiments.

Contribution

The paper presents a novel algorithm for fast computation of personalized PageRank to a target node from all sources, with theoretical analysis and practical validation.

Findings

Algorithm achieves faster computation time than previous methods.

Theoretical running time is $O(\frac{1}{\alpha \epsilon} (\frac{m}{n} + \log(n)))$.

Experimental results on Twitter graph show practical efficiency.

Abstract

Personalalized PageRank uses random walks to determine the importance or authority of nodes in a graph from the point of view of a given source node. Much past work has considered how to compute personalized PageRank from a given source node to other nodes. In this work we consider the problem of computing personalized PageRanks to a given target node from all source nodes. This problem can be interpreted as finding who supports the target or who is interested in the target. We present an efficient algorithm for computing personalized PageRank to a given target up to any given accuracy. We give a simple analysis of our algorithm's running time in both the average case and the parameterized worst-case. We show that for any graph with $n$ nodes and $m$ edges, if the target node is randomly chosen and the teleport probability $\alpha$ is given, the algorithm will compute a result with $\epsilon$ error in time $O\left(\frac{1}{\alpha \epsilon} \left(\frac{m}{n} + \log(n)\right)\right)$. This is much faster than the previously proposed method of computing personalized PageRank separately from every source node, and it is comparable to the cost of computing personalized PageRank from a single source. We present results from experiments on the Twitter graph which show that the constant factors in our running time analysis are small and our algorithm is efficient in practice.