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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1704.00633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-04-03T15:12:38Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"8b0adf74765d6dafc9e319d7badee592c2738c20cb41ba3fd90a223a5b775b7e","abstract_canon_sha256":"9eff264c64f3363d1663d98e93cb01e0b1194b9400c3934405bcef42831b8fdc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:21.769211Z","signature_b64":"iXfqCKCNfQ/6OhdvCj90Mi8wFJEsR3e1dF4TrjsX3P+uKDrV1N9UfzwOjKR03erQeknAVdkw0whWtwWGSPhZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a0efef197cf481abcea835a3ecdce0f95d74d6f31ac85fdc7570063dcf0cbfb","last_reissued_at":"2026-05-18T00:47:21.768468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:21.768468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathop{support}(y)\\subset \\mathop{support}(x)$. 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