{"paper":{"title":"Linear-Space Substring Range Counting over Polylogarithmic Alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pawe{\\l} Gawrychowski, Travis Gagie","submitted_at":"2012-02-15T05:29:25Z","abstract_excerpt":"Bille and G{\\o}rtz (2011) recently introduced the problem of substring range counting, for which we are asked to store compactly a string $S$ of $n$ characters with integer labels in ([0, u]), such that later, given an interval ([a, b]) and a pattern $P$ of length $m$, we can quickly count the occurrences of $P$ whose first characters' labels are in ([a, b]). They showed how to store $S$ in $\\Oh{n \\log n / \\log \\log n}$ space and answer queries in $\\Oh{m + \\log \\log u}$ time. We show that, if $S$ is over an alphabet of size (\\polylog (n)), then we can achieve optimal linear space. Moreover, if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3208","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"}