{"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/lightning-graph-matching","title":"Lightning graph matching","arxiv_id":"2310.14701","date":"2023-10-23","proceeding":null,"authors":["Binrui. shen","Qiang. niu","Shengxin. zhu"],"abstract":"Graph matching aims to find correspondences between two graphs. It is a fundamental task in pattern recognition. The classical spectral matching algorithm has time complexity $\\mathcal{O}(n^4)$ and space complexity $\\mathcal{O}(n^4)$, where $n$ is the number of nodes. Such a complexity limits the applicability to large-scale graph matching tasks. This paper proposes an efficient redesign of spectral matching by transforming the graph matching problem into a 1D linear assignment problem, which can be solved efficiently by sorting two $n \\times 1$ vectors. The resulting algorithm is named the lightning spectral assignment method (LiSA), which enjoys a complexity of $\\mathcal{O}(n^2)$. Numerical experiments demonstrate the efficiency and the theoretical analysis of the strategy.","url_abs":"https://arxiv.org/abs/2310.14701v3","url_pdf":"https://arxiv.org/pdf/2310.14701v3.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":"lightning-graph-matching","repo_url":"https://github.com/BinruiShen/Lightning-graph-matching","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}