{"paper":{"title":"Optimal trade-offs for pattern matching with $k$ mismatches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pawe{\\l} Gawrychowski, Przemys{\\l}aw Uzna\\'nski","submitted_at":"2017-04-05T08:45:22Z","abstract_excerpt":"Given a pattern of length $m$ and a text of length $n$, the goal in $k$-mismatch pattern matching is to compute, for every $m$-substring of the text, the exact Hamming distance to the pattern or report that it exceeds $k$. This can be solved in either $\\widetilde{O}(n \\sqrt{k})$ time as shown by Amir et al. [J. Algorithms 2004] or $\\widetilde{O}((m + k^2) \\cdot n/m)$ time due to a result of Clifford et al. [SODA 2016]. We provide a smooth time trade-off between these two bounds by designing an algorithm working in time $\\widetilde{O}( (m + k \\sqrt{m}) \\cdot n/m)$. We complement this with a mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01311","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"}