{"paper":{"title":"Sublinear Space Algorithms for the Longest Common Substring Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hjalte Wedel Vildh{\\o}j, Tatiana Starikovskaya, Tomasz Kociumaka","submitted_at":"2014-07-02T11:22:11Z","abstract_excerpt":"Given $m$ documents of total length $n$, we consider the problem of finding a longest string common to at least $d \\geq 2$ of the documents. This problem is known as the \\emph{longest common substring (LCS) problem} and has a classic $O(n)$ space and $O(n)$ time solution (Weiner [FOCS'73], Hui [CPM'92]). However, the use of linear space is impractical in many applications. In this paper we show that for any trade-off parameter $1 \\leq \\tau \\leq n$, the LCS problem can be solved in $O(\\tau)$ space and $O(n^2/\\tau)$ time, thus providing the first smooth deterministic time-space trade-off from co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0522","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"}