{"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/linear-time-sequence-comparison-using-minimal","title":"Linear-Time Sequence Comparison Using Minimal Absent Words & Applications","arxiv_id":"1506.04917","date":"2015-06-16","proceeding":null,"authors":["Maxime Crochemore","Gabriele Fici","Robert Mercaş","Solon P. Pissis"],"abstract":"Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free techniques, which are based on measures referring to the composition of sequences in terms of their constituent patterns. These measures, such as $q$-gram distance, are usually computed in time linear with respect to the length of the sequences. In this article, we focus on the complementary idea: how two sequences can be efficiently compared based on information that does not occur in the sequences. A word is an {\\em absent word} of some sequence if it does not occur in the sequence. An absent word is {\\em minimal} if all its proper factors occur in the sequence. Here we present the first linear-time and linear-space algorithm to compare two sequences by considering {\\em all} their minimal absent words. In the process, we present results of combinatorial interest, and also extend the proposed techniques to compare circular sequences.","url_abs":"http://arxiv.org/abs/1506.04917v2","url_pdf":"http://arxiv.org/pdf/1506.04917v2.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":"linear-time-sequence-comparison-using-minimal","repo_url":"https://github.com/solonas13/maw","is_official":1,"mentioned_in_paper":1,"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}