{"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/08063115","title":"Using rational numbers to key nested sets","arxiv_id":"0806.3115","date":"2008-06-19","proceeding":null,"authors":["Dan Hazel"],"abstract":"This report details the generation and use of tree node ordering keys in a single relational database table. The keys for each node are calculated from the keys of its parent, in such a way that the sort order places every node in the tree before all of its descendants and after all siblings having a lower index. The calculation from parent keys to child keys is simple, and reversible in the sense that the keys of every ancestor of a node can be calculated from that node's keys without having to consult the database. Proofs of the above properties of the key encoding process and of its correspondence to a finite continued fraction form are provided.","url_abs":"http://arxiv.org/abs/0806.3115v1","url_pdf":"http://arxiv.org/pdf/0806.3115v1.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":"08063115","repo_url":"https://github.com/agustinuslaw/MatrixTreeEncoding","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"08063115","repo_url":"https://github.com/creyes17/task-tracker","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}