On the cut-off point for combinatorial group testing Original Research Article

The following problem is known as group testing problem for n objects. Each object can be essential (defective) or non-essential (intact). The problem is to determine the set of essential objects by asking queries adaptively. A query can be identified with a set Q of objects and the query Q is answered by 1 if Q contains at least one essential object and by 0 otherwise. In the statistical setting the objects are essential, independently of each other, with a given probability p < 1 while in the combinatorial setting the number k < n of essential objects is known. The cut-off point of statistical group testing is equal to p∗ = 12 (3 − √5), i.e., the strategy of testing each object individually minimizes the average number of queries iff p ⩾ p∗ or n = 1. In the combinatorial setting the worst case number of queries is of interest. It has been conjectured that the cut-off point of combinatorial group testing is equal to x∗ = 13 i.e., the strategy of testing n − 1 objects individually minimizes the worst case number of queries iff kn ⩾ α∗ and k < n. Some results in favor of this conjecture are proved.