{"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/efficient-algorithms-for-the-longest-common","title":"Efficient algorithms for the longest common subsequence in $k$-length substrings","arxiv_id":"1311.4552","date":"2013-11-18","proceeding":null,"authors":["Sebastian Deorowicz","Szymon Grabowski"],"abstract":"Finding the longest common subsequence in $k$-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences $A$ and $B$ are replaced with matching non-overlapping substrings of length $k$ from $A$ and $B$. We propose several algorithms for LCS$k$, being non-trivial incarnations of the major concepts known from LCS research (dynamic programming, sparse dynamic programming, tabulation). Our algorithms make use of a linear-time and linear-space preprocessing finding the occurrences of all the substrings of length $k$ from one sequence in the other sequence.","url_abs":"https://arxiv.org/abs/1311.4552v1","url_pdf":"https://arxiv.org/pdf/1311.4552v1.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":"efficient-algorithms-for-the-longest-common","repo_url":"https://github.com/fpavetic/lcskpp","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}