{"paper":{"title":"Optimal Time-Space Tradeoff for Dynamic Difference-Encoded Dictionaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Guy E. Blelloch, Jingxun Liang, Renfei Zhou, William Kuszmaul, Yang Hu","submitted_at":"2026-08-06T14:20:52Z","abstract_excerpt":"The dynamic dictionary is a fundamental data structure that maintains a set $S\\subset [U]$ of size $n$ (we assume $n=U^{1-\\Theta(1)}$), supporting insertions, deletions and membership queries. Previous works mostly focused on constructing dictionaries that support operations in $O(1)$ time and use space as close to the \\emph{information-theoretic bound} of $\\log\\binom{U}{n}$ bits as possible.\n  In this paper, we study \\emph{difference-encoded} dictionaries, which are dictionaries that use space close to the gap entropy $\\text{gap}(S):=\\sum_{i=2}^{|S|}\\left(\\lceil\\log(x_i-x_{i-1}+1)\\rceil+1\\rig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06077","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.06077/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}