{"paper":{"title":"Compressed Indexing with Signature Grammars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anders Roy Christiansen, Mikko Berggren Ettienne","submitted_at":"2017-11-22T10:40:06Z","abstract_excerpt":"The compressed indexing problem is to preprocess a string $S$ of length $n$ into a compressed representation that supports pattern matching queries. That is, given a string $P$ of length $m$ report all occurrences of $P$ in $S$.\n  We present a data structure that supports pattern matching queries in $O(m + occ (\\lg\\lg n + \\lg^\\epsilon z))$ time using $O(z \\lg(n / z))$ space where $z$ is the size of the LZ77 parse of $S$ and $\\epsilon > 0$ is an arbitrarily small constant, when the alphabet is small or $z = O(n^{1 - \\delta})$ for any constant $\\delta > 0$. We also present two data structures fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08217","kind":"arxiv","version":3},"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"}