{"paper":{"title":"Hardness of Bichromatic Closest Pair with Jaccard Similarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Mikkel Thorup, Nina Stausholm, Rasmus Pagh","submitted_at":"2019-07-04T07:03:53Z","abstract_excerpt":"Consider collections $\\mathcal{A}$ and $\\mathcal{B}$ of red and blue sets, respectively. Bichromatic Closest Pair is the problem of finding a pair from $\\mathcal{A}\\times \\mathcal{B}$ that has similarity higher than a given threshold according to some similarity measure. Our focus here is the classic Jaccard similarity $|\\textbf{a}\\cap \\textbf{b}|/|\\textbf{a}\\cup \\textbf{b}|$ for $(\\textbf{a},\\textbf{b})\\in \\mathcal{A}\\times \\mathcal{B}$.\n  We consider the approximate version of the problem where we are given thresholds $j_1>j_2$ and wish to return a pair from $\\mathcal{A}\\times \\mathcal{B}$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02251","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"}