{"paper":{"title":"Linear-Time Algorithm for Long LCF with $k$ Mismatches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Costas S. Iliopoulos, Jakub Radoszewski, Maxime Crochemore, Panagiotis Charalampopoulos, Solon P. Pissis, Tomasz Kociumaka, Tomasz Wale\\'n, Wojciech Rytter","submitted_at":"2018-02-18T13:04:21Z","abstract_excerpt":"In the Longest Common Factor with $k$ Mismatches (LCF$_k$) problem, we are given two strings $X$ and $Y$ of total length $n$, and we are asked to find a pair of maximal-length factors, one of $X$ and the other of $Y$, such that their Hamming distance is at most $k$. Thankachan et al. show that this problem can be solved in $\\mathcal{O}(n \\log^k n)$ time and $\\mathcal{O}(n)$ space for constant $k$. We consider the LCF$_k$($\\ell$) problem in which we assume that the sought factors have length at least $\\ell$, and the LCF$_k$($\\ell$) problem for $\\ell=\\Omega(\\log^{2k+2} n)$, which we call the Lon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06369","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}