{"paper":{"title":"Tight Bounds for Classical Open Addressing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael A. Bender, Renfei Zhou, William Kuszmaul","submitted_at":"2024-09-17T15:36:06Z","abstract_excerpt":"We introduce a classical open-addressed hash table, called rainbow hashing, that supports a load factor of up to $1 - \\varepsilon$, while also supporting $O(1)$ expected-time queries, and $O(\\log \\log \\varepsilon^{-1})$ expected-time insertions and deletions. We further prove that this tradeoff curve is optimal: any classical open-addressed hash table that supports load factor $1 - \\varepsilon$ must incur $\\Omega(\\log \\log \\varepsilon^{-1})$ expected time per operation.\n  Finally, we extend rainbow hashing to the setting where the hash table is dynamically resized over time. Surprisingly, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.11280","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/2409.11280/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"}