{"paper":{"title":"A Simple Hash Class with Strong Randomness Properties in Graphs and Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Martin Aum\\\"uller, Martin Dietzfelbinger, Philipp Woelfel","submitted_at":"2016-10-31T20:20:21Z","abstract_excerpt":"We study randomness properties of graphs and hypergraphs generated by simple hash functions. Several hashing applications can be analyzed by studying the structure of $d$-uniform random ($d$-partite) hypergraphs obtained from a set $S$ of $n$ keys and $d$ randomly chosen hash functions $h_1,\\dots,h_d$ by associating each key $x\\in S$ with a hyperedge $\\{h_1(x),\\dots, h_d(x)\\}$. Often it is assumed that $h_1,\\dots,h_d$ exhibit a high degree of independence. We present a simple construction of a hash class whose hash functions have small constant evaluation time and can be stored in sublinear sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00029","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"}