{"paper":{"title":"Power of $d$ Choices with Simple Tabulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anders Aamand, Mathias B{\\ae}k Tejs Knudsen, Mikkel Thorup","submitted_at":"2018-04-25T17:23:48Z","abstract_excerpt":"Suppose that we are to place $m$ balls into $n$ bins sequentially using the $d$-choice paradigm: For each ball we are given a choice of $d$ bins, according to $d$ hash functions $h_1,\\dots,h_d$ and we place the ball in the least loaded of these bins breaking ties arbitrarily. Our interest is in the number of balls in the fullest bin after all $m$ balls have been placed.\n  Azar et al. [STOC'94] proved that when $m=O(n)$ and when the hash functions are fully random the maximum load is at most $\\frac{\\lg \\lg n }{\\lg d}+O(1)$ whp (i.e. with probability $1-O(n^{-\\gamma})$ for any choice of $\\gamma$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09684","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"}