{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/accelerating-personalized-pagerank-vector","title":"Accelerating Personalized PageRank Vector Computation","arxiv_id":"2306.02102","date":"2023-06-03","proceeding":null,"authors":["Zhen Chen","Xingzhi Guo","Baojian Zhou","Deqing Yang","Steven Skiena"],"abstract":"Personalized PageRank Vectors are widely used as fundamental graph-learning tools for detecting anomalous spammers, learning graph embeddings, and training graph neural networks. The well-known local FwdPush algorithm approximates PPVs and has a sublinear rate of $O\\big(\\frac{1}{\\alpha\\epsilon}\\big)$. A recent study found that when high precision is required, FwdPush is similar to the power iteration method, and its run time is pessimistically bounded by $O\\big(\\frac{m}{\\alpha} \\log\\frac{1}{\\epsilon}\\big)$. This paper looks closely at calculating PPVs for both directed and undirected graphs. By leveraging the linear invariant property, we show that FwdPush is a variant of Gauss-Seidel and propose a Successive Over-Relaxation based method, FwdPushSOR to speed it up by slightly modifying FwdPush. Additionally, we prove FwdPush has local linear convergence rate $O\\big(\\tfrac{\\text{vol}(S)}{\\alpha} \\log\\tfrac{1}{\\epsilon}\\big)$ enjoying advantages of two existing bounds. We also design a new local heuristic push method that reduces the number of operations by 10-50 percent compared to FwdPush. For undirected graphs, we propose two momentum-based acceleration methods that can be expressed as one-line updates and speed up non-acceleration methods by$\\mathcal{O}\\big(\\tfrac{1}{\\sqrt{\\alpha}}\\big)$. Our experiments on six real-world graph datasets confirm the efficiency of FwdPushSOR and the acceleration methods for directed and undirected graphs, respectively.","url_abs":"https://arxiv.org/abs/2306.02102v2","url_pdf":"https://arxiv.org/pdf/2306.02102v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"accelerating-personalized-pagerank-vector","repo_url":"https://github.com/ccczhen/accppr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2306.02102","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}