{"paper":{"title":"Optimal searching of gapped repeats in a word","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Gregory Kucherov, Maxime Crochemore, Roman Kolpakov","submitted_at":"2015-09-03T19:11:14Z","abstract_excerpt":"Following (Kolpakov et al., 2013; Gawrychowski and Manea, 2015), we continue the study of {\\em $\\alpha$-gapped repeats} in strings, defined as factors $uvu$ with $|uv|\\leq \\alpha |u|$. Our main result is the $O(\\alpha n)$ bound on the number of {\\em maximal} $\\alpha$-gapped repeats in a string of length $n$, previously proved to be $O(\\alpha^2 n)$ in (Kolpakov et al., 2013). For a closely related notion of maximal $\\delta$-subrepetition (maximal factors of exponent between $1+\\delta$ and $2$), our result implies the $O(n/\\delta)$ bound on their number, which improves the bound of (Kolpakov et "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01221","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"}