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The approximation ratio for $\\arrowvert A_1\\cup A_2\\cup...\\cup A_m\\arrowvert$ is in the range $[(1-\\epsilon)(1-\\alpha_L)(1-"},"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":"1802.06204","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-17T07:37:40Z","cross_cats_sorted":["cs.CC","cs.CG","cs.DM"],"title_canon_sha256":"d0a8cdab5d3a1c1dc0ea7d1045209ada65bca49da941e49cce7b53f316605495","abstract_canon_sha256":"de215e2d9acf2890c76bfe7c9ad73ad5f39974d8565deb0f38414e04e7f5ef89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:10.411572Z","signature_b64":"FhPcwVe27Br4C9GEMze1waKdPD5DcLYFPnZSriPzizuVKQsz7IJG7xyYMMGXB2yY/rmfBKoDgPKw6DRyxrUkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0330fea8fb652b124c2857849df49390949ef2eb8c5c4b65ac8ef1dea3518675","last_reissued_at":"2026-05-18T00:13:10.410853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:10.410853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximate Set Union Via Approximate Randomization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CG","cs.DM"],"primary_cat":"cs.DS","authors_text":"Bin Fu, Pengfei Gu, Yuming Zhao","submitted_at":"2018-02-17T07:37:40Z","abstract_excerpt":"We develop an randomized approximation algorithm for the size of set union problem $\\arrowvert A_1\\cup A_2\\cup...\\cup A_m\\arrowvert$, which given a list of sets $A_1,...,A_m$ with approximate set size $m_i$ for $A_i$ with $m_i\\in \\left((1-\\beta_L)|A_i|, (1+\\beta_R)|A_i|\\right)$, and biased random generators with $Prob(x=\\randomElm(A_i))\\in \\left[{1-\\alpha_L\\over |A_i|},{1+\\alpha_R\\over |A_i|}\\right]$ for each input set $A_i$ and element $x\\in A_i,$ where $i=1, 2, ..., m$. 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