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

Dec 2022

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

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