{"paper":{"title":"Approximate Range Emptiness in Constant Time and Optimal Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Allan Gr{\\o}nlund, Kasper Green Larsen, Mayank Goswami, Rasmus Pagh","submitted_at":"2014-07-10T19:14:59Z","abstract_excerpt":"This paper studies the \\emph{$\\varepsilon$-approximate range emptiness} problem, where the task is to represent a set $S$ of $n$ points from $\\{0,\\ldots,U-1\\}$ and answer emptiness queries of the form \"$[a ; b]\\cap S \\neq \\emptyset$ ?\" with a probability of \\emph{false positives} allowed. This generalizes the functionality of \\emph{Bloom filters} from single point queries to any interval length $L$. Setting the false positive rate to $\\varepsilon/L$ and performing $L$ queries, Bloom filters yield a solution to this problem with space $O(n \\lg(L/\\varepsilon))$ bits, false positive probability b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2907","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"}