On Competitive Group Testing

In many fault detection problems, the goal is to identify defective items from a set of items with a minimum number of tests. Each test is on a subset of items, which tells whether the subset contains a defective item or not. The concept of competitive algorithm has been developed to relate the properties of the group testing algorithms that assume that the number of defective items $d$ is known, to those without any a priori knowledge on $d$. A new concept of strongly competitive algorithm is defined that relates different characteristics of these two classes of algorithms and present an interesting relationship between the two concepts competitive and strongly competitive. A strongly competitive algorithm is also presented.