Threshold and majority group testing R. Ahlswede a , C. Deppe a , V. Lebedev b a Department of Mathematics, University of Bielefeld b IPPI (Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)) Abstract We consider two generalizations of group testing: threshold group testing (introduced by Damaschke [7]) and majority group testing (a further gen- eralization, including threshold group testing and a model introduced by Lebedev [14]). We show that each separating code gives a nonadaptive strategy for threshold group testing for some parameters. This is a generalization of a result in [2] on “guessing secrets”, introduced in [5]. We introduce threshold codes and show that each threshold code gives a nonadaptive strategy for threshold group testing. We show that there exist threshold codes such that we can improve the lower bound of [3] for the rate of threshold group testing. We consider majority group testing if the number of defective elements is unknown (otherwise it reduces to threshold group testing). We show that cover-free codes and separating codes give strategies for majority group test- ing. We give a lower bound for the rate of majority group testing. Keywords: group testing, pooling, threshold group testing, separating codes, cover-free codes 1 Email addresses: ahlswede@math.uni-bielfeld.de (R. Ahlswede), cdeppe@math.uni-bielfeld.de (C. Deppe), lebedev37@mail.ru (V. Lebedev) Supported by the DFG in the project “Advances in Search and Sorting” Supported in part by the Russian Foundation for Basic Research, project no 09-01- 00536. Preprint submitted to Elsevier January 25, 2011