{"paper":{"title":"Constant factor approximations to edit distance on far input pairs in nearly linear time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael E. Saks, Michal Kouck\\'y","submitted_at":"2019-04-10T21:52:07Z","abstract_excerpt":"For any $T \\geq 1$, there are constants $R=R(T) \\geq 1$ and $\\zeta=\\zeta(T)>0$ and a randomized algorithm that takes as input an integer $n$ and two strings $x,y$ of length at most $n$, and runs in time $O(n^{1+\\frac{1}{T}})$ and outputs an upper bound $U$ on the edit distance $ED(x,y)$ that with high probability, satisfies $U \\leq R(ED(x,y)+n^{1-\\zeta})$. In particular, on any input with $ED(x,y) \\geq n^{1-\\zeta}$ the algorithm outputs a constant factor approximation with high probability.\n  A similar result has been proven independently by Brakensiek and Rubinstein (2019)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05459","kind":"arxiv","version":2},"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"}