{"paper":{"title":"Counting Colours in Compressed Strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Juha K\\\"arkk\\\"ainen, Travis Gagie","submitted_at":"2010-11-15T19:30:19Z","abstract_excerpt":"Suppose we are asked to preprocess a string \\(s [1..n]\\) such that later, given a substring's endpoints, we can quickly count how many distinct characters it contains. In this paper we give a data structure for this problem that takes \\(n H_0 (s) + \\Oh{n} + \\oh{n H_0 (s)}\\) bits, where \\(H_0 (s)\\) is the 0th-order empirical entropy of $s$, and answers queries in $\\Oh{\\log^{1 + \\epsilon} n}$ time for any constant \\(\\epsilon > 0\\). We also show how our data structure can be made partially dynamic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3480","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"}