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So far, the only subquadratic time result for this problem was known for $k = 1$~\\cite{FGKU2014}. We first present two output-dependent algorithms solving the $k$-LCF problem and show that for $k = O(\\log^{1-\\varepsilon} n)$, where $\\varepsilon > 0$, at least one of them works in subquadratic time, using $O(n)$ words o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.7217","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-09-25T11:29:18Z","cross_cats_sorted":[],"title_canon_sha256":"6b987070e36e1a782a7cdd7ae05bc5d71f51660ba6851dcf7b8690f9ca49d0f2","abstract_canon_sha256":"d2da2d07d03b40d0b59ca536b9765b2cf2f9f614046b434d7cb55e471d463f12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:09.816915Z","signature_b64":"S0LUEWfLm+18YBUSg0GpCoJEWhnVTvJQ6khXFhybKSFVwVCfzYZaLahAgMSMXcND+c8bLXy21DRUwqUYgAGaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea2f402f31363a9e7aff8bdf5f2a1c5944b3528c50a4ba42ae2bd83edf9aaf03","last_reissued_at":"2026-05-18T02:40:09.816476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:09.816476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the longest common substring with $k$-mismatches problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Szymon Grabowski","submitted_at":"2014-09-25T11:29:18Z","abstract_excerpt":"The recently introduced longest common substring with $k$-mismatches ($k$-LCF) problem is to find, given two sequences $S_1$ and $S_2$ of length $n$ each, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance between $A_1$ and $A_2$ is at most $k$. 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