Personalized PageRank on Evolving Graphs with an Incremental Index-Update Scheme

TL;DR

This paper introduces an efficient incremental indexing scheme for Personalized PageRank on evolving graphs, achieving constant-time updates and significantly improving over existing methods without losing query accuracy.

Contribution

It proposes a novel incremental index-update scheme for Personalized PageRank that operates in expected O(1) time per update on dynamic graphs.

Findings

Achieves orders of magnitude faster update times than existing methods

Supports approximate Personalized PageRank queries with guarantees

Reduces space consumption with a new sampling scheme

Abstract

{\em Personalized PageRank (PPR)} stands as a fundamental proximity measure in graph mining. Since computing an exact SSPPR query answer is prohibitive, most existing solutions turn to approximate queries with guarantees. The state-of-the-art solutions for approximate SSPPR queries are index-based and mainly focus on static graphs, while real-world graphs are usually dynamically changing. However, existing index-update schemes can not achieve a sub-linear update time. Motivated by this, we present an efficient indexing scheme to maintain indexed random walks in expected $O(1)$ time after each graph update. To reduce the space consumption, we further propose a new sampling scheme to remove the auxiliary data structure for vertices while still supporting $O(1)$ index update cost on evolving graphs. Extensive experiments show that our update scheme achieves orders of magnitude speed-up on update performance over existing index-based dynamic schemes without sacrificing the query efficiency.