{"paper":{"title":"Approximate pattern matching with k-mismatches in packed text","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Emanuele Giaquinta, Kimmo Fredriksson, Szymon Grabowski","submitted_at":"2012-11-23T08:30:45Z","abstract_excerpt":"Given strings $P$ of length $m$ and $T$ of length $n$ over an alphabet of size $\\sigma$, the string matching with $k$-mismatches problem is to find the positions of all the substrings in $T$ that are at Hamming distance at most $k$ from $P$. If $T$ can be read only one character at the time the best known bounds are $O(n\\sqrt{k\\log k})$ and $O(n + n\\sqrt{k/w}\\log k)$ in the word-RAM model with word length $w$. In the RAM models (including $AC^0$ and word-RAM) it is possible to read up to $\\floor{w / \\log \\sigma}$ characters in constant time if the characters of $T$ are encoded using $\\ceil{\\lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5433","kind":"arxiv","version":3},"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"}