{"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/unifying-the-global-and-local-approaches-an","title":"Unifying the Global and Local Approaches: An Efficient Power Iteration with Forward Push","arxiv_id":"2101.03652","date":"2021-01-11","proceeding":null,"authors":["Hao Wu","Junhao Gan","Zhewei Wei","Rui Zhang"],"abstract":"Personalized PageRank (PPR) is a critical measure of the importance of a node t to a source node s in a graph. The Single-Source PPR (SSPPR) query computes the PPR's of all the nodes with respect to s on a directed graph $G$ with $n$ nodes and $m$ edges, and it is an essential operation widely used in graph applications. In this paper, we propose novel algorithms for solving two variants of SSPPR: (i) high-precision queries and (ii) approximate queries. For high-precision queries, Power Iteration (PowItr) and Forward Push (FwdPush) are two fundamental approaches. Given an absolute error threshold $\\lambda$, the only known bound of FwdPush is $O(\\frac{m}{\\lambda})$, much worse than the $O(m \\log \\frac{1}{\\lambda})$-bound of PowItr. Whether FwdPush can achieve the same running time bound as PowItr does still remains an open question in the research community. We give a positive answer to this question by showing that the running time of a common implementation of FwdPush is actually bounded by $O(m \\cdot \\log \\frac{1}{\\lambda})$.Based on this finding, we propose a new algorithm, called Power Iteration with Forward Push (PowerPush), which incorporates the strengths of both PowItr and FwdPush. For approximate queries (with a relative error $\\epsilon$), we propose a new algorithm, called SpeedPPR, with overall expected time bounded by $O(n \\cdot \\log n \\cdot \\log \\frac{1}{\\epsilon})$ on scale-free graphs. This bound greatly improves the $O(\\frac{n \\cdot \\log n}{\\epsilon})$ bound of a state-of-the-art algorithm FORA.","url_abs":"https://arxiv.org/abs/2101.03652v2","url_pdf":"https://arxiv.org/pdf/2101.03652v2.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":"unifying-the-global-and-local-approaches-an","repo_url":"https://github.com/wuhao-wu-jiang/Personalized-PageRank","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2101.03652","atlas_url":"https://app.syntology.ai/?focus=2101.03652","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}