{"paper":{"title":"Alphabet-Dependent String Searching with Wexponential Search Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Johannes Fischer, Pawel Gawrychowski","submitted_at":"2013-02-14T09:29:09Z","abstract_excerpt":"It is widely assumed that $O(m+\\lg \\sigma)$ is the best one can do for finding a pattern of length $m$ in a compacted trie storing strings over an alphabet of size $\\sigma$, if one insists on linear-size data structures and deterministic worst-case running times [Cole et al., ICALP'06]. In this article, we first show that a rather straightforward combination of well-known ideas yields $O(m+\\lg\\lg \\sigma)$ deterministic worst-case searching time for static tries.\n  Then we move on to dynamic tries, where we achieve a worst-case bound of $O(m+\\frac{\\lg^{2}\\lg\\sigma}{\\lg\\lg\\lg\\sigma})$ per query "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3347","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"}