{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZME7DVVJBHUJVE3I4PMUAWXDYI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a8ecfb4f82d06b9bdc7512d93af0712acde209f30c8e45479a0ad32183161539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-03T20:37:41Z","title_canon_sha256":"d1cae2691fabc0a533ae92dc0d64a4d456a827309bd9c3c869db704d18c4f1ba"},"schema_version":"1.0","source":{"id":"1503.01093","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01093","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01093v3","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01093","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZME7DVVJBHUJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZME7DVVJBHUJVE3I","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZME7DVVJ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:672f060bef81b116642b26403c7fd4d2a3e03e3ff0bf8b407d45b8145991c358","target":"graph","created_at":"2026-05-18T02:25:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Abelian string matching problems are becoming an object of considerable interest in last years. Very recently, Alatabbi et al. \\cite{AILR2015} presented the first solution for the longest common Abelian factor problem for a pair of strings, reaching $O(\\sigma n^2)$ time with $O(\\sigma n \\log n)$ bits of space, where $n$ is the length of the strings and $\\sigma$ is the alphabet size. In this note we show how the time complexity can be preserved while the space is reduced by a factor of $\\sigma$, and then how the time complexity can be improved, if the alphabet is not too small, when superlinear","authors_text":"Szymon Grabowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-03T20:37:41Z","title":"A note on the longest common Abelian factor problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01093","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6dccfdaf99ceb7bd5410863330b800cf4e913ca1d53efbb1f916755bdf32713b","target":"record","created_at":"2026-05-18T02:25:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a8ecfb4f82d06b9bdc7512d93af0712acde209f30c8e45479a0ad32183161539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-03T20:37:41Z","title_canon_sha256":"d1cae2691fabc0a533ae92dc0d64a4d456a827309bd9c3c869db704d18c4f1ba"},"schema_version":"1.0","source":{"id":"1503.01093","kind":"arxiv","version":3}},"canonical_sha256":"cb09f1d6a909e89a9368e3d9405ae3c20df1d2984555a886d7eb7ccb08769a9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb09f1d6a909e89a9368e3d9405ae3c20df1d2984555a886d7eb7ccb08769a9d","first_computed_at":"2026-05-18T02:25:04.368815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:04.368815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hLLW4BAtJdG/WawmMWrpHbBkYXoKdebgV+mzgD5nKRhqNJmiHL/W5dTHMuLupQHNQcPIGStx9i7chQCQ7ZEoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:04.369167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01093","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dccfdaf99ceb7bd5410863330b800cf4e913ca1d53efbb1f916755bdf32713b","sha256:672f060bef81b116642b26403c7fd4d2a3e03e3ff0bf8b407d45b8145991c358"],"state_sha256":"b4b2921d6c1c0e1e2e078e34977a1ff093a04c62627fd4972ffb6816da746064"}