{"paper":{"title":"Quantitative Group Testing and the rank of random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amir Lellouche, Uriel Feige","submitted_at":"2020-06-16T11:08:22Z","abstract_excerpt":"Given a random Bernoulli matrix $ A\\in \\{0,1\\}^{m\\times n} $, an integer $ 0< k < n $ and the vector $ y:=Ax $, where $ x \\in \\{0,1\\}^n $ is of Hamming weight $ k $, the objective in the {\\em Quantitative Group Testing} (QGT) problem is to recover $ x $. This problem is more difficult the smaller $m$ is. For parameter ranges of interest to us, known polynomial time algorithms require values of $m$ that are much larger than $k$.\n  In this work, we define a seemingly easier problem that we refer to as {\\em Subset Select}. Given the same input as in QGT, the objective in Subset Select is to retur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.09074","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.09074/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}