{"paper":{"title":"Approximating Approximate Pattern Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jan Studen\\'y, Przemys{\\l}aw Uzna\\'nski","submitted_at":"2018-10-03T10:38:59Z","abstract_excerpt":"Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the approximate pattern matching problem asks for computation of a particular \\emph{distance} function between $P$ and every $m$-substring of $T$. We consider a $(1\\pm\\varepsilon)$ multiplicative approximation variant of this problem, for $\\ell_p$ distance function. In this paper, we describe two $(1+\\varepsilon)$-approximate algorithms with a runtime of $\\widetilde{O}(\\frac{n}{\\varepsilon})$ for all (constant) non-negative values of $p$. For constant $p \\ge 1$ we show a deterministic $(1+\\varepsilon)$-approximation algorithm. Pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01676","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"}