Trivial two-stage group testing for complexes using almost disjunct matrices.
Given \(t\) items with \(k\) unknown positive ones, the group testing problem is asking to identify all \(k\) positive items with a less number of tests each of which is on a subset of items and tells whether the subset contains a positive item or not. Consider a hypergraph with all \(k\)-subsets as its hyperedges and \(t\) items as its vertices. All \(k\) positive items form a positive hyperedge. Each test would tell whether the tested subset is incident to the positive hyperedge or not. The problem studied in this paper is a generalization of dual group testing problem. First, each test outcome is whether a subset contains a positive hyperedge or not, which is a dual test model in group testing. Secondly, there is not only one positive hyperedge. In this paper, the authors present a two-stage algorithm for identifying all positive hyperedges. (The hyperedge is called complex in this paper.)
scientific article; zbMATH DE number 2041890