{"paper":{"title":"A note on the longest common Abelian factor problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Szymon Grabowski","submitted_at":"2015-03-03T20:37:41Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01093","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"}