{"paper":{"title":"On the Parallel Reconstruction from Pooled Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DM","authors_text":"Dominik Kaaser, Max Hahn-Klimroth, Oliver Gebhard, Philipp Loick","submitted_at":"2019-05-04T08:57:34Z","abstract_excerpt":"In the pooled data problem the goal is to efficiently reconstruct a binary signal from additive measurements. Given a signal $\\sigma \\in \\{ 0,1 \\}^n$, we can query multiple entries at once and get the total number of non-zero entries in the query as a result. We assume that queries are time-consuming and therefore focus on the setting where all queries are executed in parallel. For the regime where the signal is sparse such that $ || \\sigma ||_1 = o(n)$ our results are twofold: First, we propose and analyze a simple and efficient greedy reconstruction algorithm. Secondly, we derive a sharp inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01458","kind":"arxiv","version":4},"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/1905.01458/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"}