{"paper":{"title":"Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Bhaskar Ray Chaudhury, Karl Bringmann","submitted_at":"2018-10-02T13:42:21Z","abstract_excerpt":"We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a sketch size and streaming space usage of $\\mathcal{O}(L^{|\\Sigma| - 1} \\log L)$.\n  We also prove matching unconditional lower bounds.\n  As an application, we study a variant of LCS where each alphabet symbol is equipped with a weight that is given as input, and the task is to compute a common subsequence of maximum total weight. Using our sketching algorithm, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01238","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"}