{"paper":{"title":"Streaming Periodicity with Mismatches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Elena Grigorescu, Erfan Sadeqi Azer, Funda Erg\\\"un, Samson Zhou","submitted_at":"2017-08-15T02:12:48Z","abstract_excerpt":"We study the problem of finding all $k$-periods of a length-$n$ string $S$, presented as a data stream. $S$ is said to have $k$-period $p$ if its prefix of length $n-p$ differs from its suffix of length $n-p$ in at most $k$ locations.\n  We give a one-pass streaming algorithm that computes the $k$-periods of a string $S$ using $\\text{poly}(k, \\log n)$ bits of space, for $k$-periods of length at most $\\frac{n}{2}$. We also present a two-pass streaming algorithm that computes $k$-periods of $S$ using $\\text{poly}(k, \\log n)$ bits of space, regardless of period length. We complement these results "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04381","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"}