{"paper":{"title":"Efficiently Decodable Non-Adaptive Threshold Group Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Isao Echizen, Mahdi Cheraghchi, Minoru Kuribayashi, Thach V. Bui","submitted_at":"2017-12-20T14:57:57Z","abstract_excerpt":"We consider non-adaptive threshold group testing for identification of up to $d$ defective items in a set of $n$ items, where a test is positive if it contains at least $2 \\leq u \\leq d$ defective items, and negative otherwise. The defective items can be identified using $t = O \\left( \\left( \\frac{d}{u} \\right)^u \\left( \\frac{d}{d - u} \\right)^{d-u} \\left(u \\log{\\frac{d}{u}} + \\log{\\frac{1}{\\epsilon}} \\right) \\cdot d^2 \\log{n} \\right)$ tests with probability at least $1 - \\epsilon$ for any $\\epsilon > 0$ or $t = O \\left( \\left( \\frac{d}{u} \\right)^u \\left( \\frac{d}{d -u} \\right)^{d - u} d^3 \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07509","kind":"arxiv","version":8},"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"}