{"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 $i=1, 2, ..., m$. 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-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06204","kind":"arxiv","version":3},"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"}