{"paper":{"title":"Optimal lower bounds for universal relation, and for samplers and finding duplicates in streams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"David P. Woodruff, Jakub Pachocki, Jelani Nelson, Michael Kapralov, Mobin Yahyazadeh, Zhengyu Wang","submitted_at":"2017-04-03T15:12:38Z","abstract_excerpt":"In the communication problem $\\mathbf{UR}$ (universal relation) [KRW95], Alice and Bob respectively receive $x, y \\in\\{0,1\\}^n$ with the promise that $x\\neq y$. The last player to receive a message must output an index $i$ such that $x_i\\neq y_i$. We prove that the randomized one-way communication complexity of this problem in the public coin model is exactly $\\Theta(\\min\\{n,\\log(1/\\delta)\\log^2(\\frac n{\\log(1/\\delta)})\\})$ for failure probability $\\delta$. Our lower bound holds even if promised $\\mathop{support}(y)\\subset \\mathop{support}(x)$. As a corollary, we obtain optimal lower bounds fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00633","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"}