{"paper":{"title":"Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CG","cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Huacheng Yu, Kasper Green Larsen, Omri Weinstein","submitted_at":"2017-03-10T08:35:24Z","abstract_excerpt":"This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds.\n  We introduce a new method for proving dynamic cell probe lower bounds and use it to prove a $\\tilde{\\Omega}(\\log^{1.5} n)$ lower bound on the operational time of a wide range of boolean data structure problems, most notably, on the query time of dynamic range counting over $\\mathbb{F}_2$ ([Pat07]). Proving an $\\omega(\\lg n)$ lower bound for this problem was explicitly posed as one of fiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03575","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"}