{"paper":{"title":"On Two LZ78-style Grammars: Compression Bounds and Compressed-Space Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dmitry Kosolobov, Golnaz Badkobeh, Shunsuke Inenaga, Simon J. Puglisi, Tomasz Kociumaka, Travis Gagie","submitted_at":"2017-05-26T11:33:05Z","abstract_excerpt":"We investigate two closely related LZ78-based compression schemes: LZMW (an old scheme by Miller and Wegman) and LZD (a recent variant by Goto et al.). Both LZD and LZMW naturally produce a grammar for a string of length $n$; we show that the size of this grammar can be larger than the size of the smallest grammar by a factor $\\Omega(n^{\\frac{1}3})$ but is always within a factor $O((\\frac{n}{\\log n})^{\\frac{2}{3}})$. In addition, we show that the standard algorithms using $\\Theta(z)$ working space to construct the LZD and LZMW parsings, where $z$ is the size of the parsing, work in $\\Omega(n^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09538","kind":"arxiv","version":2},"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"}