{"paper":{"title":"Faster Recovery of Approximate Periods over Edit Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jakub Radoszewski, Juliusz Straszy\\'nski, Tomasz Kociumaka, Tomasz Wale\\'n, Wiktor Zuba, Wojciech Rytter","submitted_at":"2018-07-27T08:16:29Z","abstract_excerpt":"The approximate period recovery problem asks to compute all $\\textit{approximate word-periods}$ of a given word $S$ of length $n$: all primitive words $P$ ($|P|=p$) which have a periodic extension at edit distance smaller than $\\tau_p$ from $S$, where $\\tau_p = \\lfloor \\frac{n}{(3.75+\\epsilon)\\cdot p} \\rfloor$ for some $\\epsilon>0$. Here, the set of periodic extensions of $P$ consists of all finite prefixes of $P^\\infty$.\n  We improve the time complexity of the fastest known algorithm for this problem of Amir et al. [Theor. Comput. Sci., 2018] from $O(n^{4/3})$ to $O(n \\log n)$. Our tool is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10483","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"}