Randomized group testing for mutually obscuring defectives

Abstract

We consider a version of the well-known group testing problem with several sorts of defectives which may mutually disturb their detection in any test. There are some nice motivations, including test planning, the counterfeit coin puzzle, and learning Boolean function with few relevant attributes. If we have no previous knowledge about the number of defectives, it requires linearly many tests to find all defectives certainly. In contrast we present a randomized strategy with a test number exceeding the information-theoretic lower bound only by a constant factor. This result is obtained by standard techniques. On the other hand, since the problem is not comparable to classical group testing, the result cannot be derived from the known deterministic results on competitive group testing. © 1998 Elsevier Science B.V. All rights reserved.