{"paper":{"title":"Faster Compact On-Line Lempel-Ziv Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hideo Bannai, Jun'ichi Yamamoto, Masayuki Takeda, Shunsuke Inenaga, Tomohiro I","submitted_at":"2013-05-27T02:35:15Z","abstract_excerpt":"We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in $O(N\\log N)$ time and uses only $O(N\\log\\sigma)$ bits of working space, where $N$ is the length of the string and $\\sigma$ is the size of the alphabet. This is a notable improvement compared to the performance of previous on-line algorithms using the same order of working space but running in either $O(N\\log^3N)$ time (Okanohara & Sadakane 2009) or $O(N\\log^2N)$ time (Starikovskaya 2012). The key to our new algorithm is in the utilization of an elegant but less popular index structure called "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6095","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"}