{"paper":{"title":"Top-Down Skiplists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Luis Barba, Pat Morin","submitted_at":"2014-07-30T01:24:34Z","abstract_excerpt":"We describe todolists (top-down skiplists), a variant of skiplists (Pugh 1990) that can execute searches using at most $\\log_{2-\\varepsilon} n + O(1)$ binary comparisons per search and that have amortized update time $O(\\varepsilon^{-1}\\log n)$. A variant of todolists, called working-todolists, can execute a search for any element $x$ using $\\log_{2-\\varepsilon} w(x) + o(\\log w(x))$ binary comparisons and have amortized search time $O(\\varepsilon^{-1}\\log w(w))$. Here, $w(x)$ is the \"working-set number\" of $x$. No previous data structure is known to achieve a bound better than $4\\log_2 w(x)$ c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7917","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"}