{"paper":{"title":"Near-Optimal Quantum Algorithm for Finding the Longest Common Substring between Run-Length Encoded Strings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Han-Hsuan Lin, Tzu-Ching Lee","submitted_at":"2024-10-21T15:52:08Z","abstract_excerpt":"We give a near-optimal quantum algorithm for the longest common substring (LCS) problem between two run-length encoded (RLE) strings, with the assumption that the prefix-sums of the run-lengths are given.\n  Our algorithm costs $\\tilde{\\mathcal{O}}(n^{2/3}/d^{1/6-o(1)}\\cdot\\mathrm{polylog}(\\tilde{n}))$ time, while the query lower bound for the problem is $\\tilde{\\Omega}(n^{2/3}/d^{1/6})$, where $n$ and $\\tilde{n}$ are the encoded and decoded length of the inputs, respectively, and $d$ is the encoded length of the LCS.\n  We justify the use of prefix-sum oracles for two reasons. First, we note th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02421","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.02421/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}