{"paper":{"title":"Succinct Choice Dictionaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Frank Kammer, Torben Hagerup","submitted_at":"2016-04-20T18:52:00Z","abstract_excerpt":"The choice dictionary is introduced as a data structure that can be initialized with a parameter $n\\in\\mathbb{N}=\\{1,2,\\ldots\\}$ and subsequently maintains an initially empty subset $S$ of $\\{1,\\ldots,n\\}$ under insertion, deletion, membership queries and an operation choice that returns an arbitrary element of $S$. The choice dictionary appears to be fundamental in space-efficient computing. We show that there is a choice dictionary that can be initialized with $n$ and an additional parameter $t\\in\\mathbb{N}$ and subsequently occupies $n+O(n(t/w)^t+\\log n)$ bits of memory and executes each of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06058","kind":"arxiv","version":3},"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"}