{"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/a-class-of-orders-with-linear-time-sorting","title":"A class of orders with linear? time sorting algorithm","arxiv_id":"1809.00954","date":"2018-09-04","proceeding":null,"authors":["Laurent Lyaudet"],"abstract":"In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true result of this article is an efficient universality result for lexicographic order, or more generally for some linear extensions of the partial order `Next': `if current items are equal, compare next items'. We define new classes of orders: (Finite width) Tree Structured Orders. We show that an instance of a finite width tree structured order can be converted in linear time and space to an instance of lexicographic order. The constants implied by the `nextification' algorithm are small (around 3 for real world orders). The class of finite width tree structured orders contains finite orders ({0, 1}, int32, int64, ..., float, double, ...), and orders constructed from them on a tree structure. In particular, unbounded integers, strings with arbitrary collation, and all orders used for sorting SQL queries are finite width tree structured orders.","url_abs":"http://arxiv.org/abs/1809.00954v5","url_pdf":"http://arxiv.org/pdf/1809.00954v5.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":"a-class-of-orders-with-linear-time-sorting","repo_url":"https://github.com/LLyaudet/TSODLULS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}