A Zig-Zag Approach for Competitive Group Testing

In many fault-detection problems, we want to identify defective items from a set of n items using the minimum number of tests. Group testing is a scenario in which each test is on a subset of items and determines whether the subset contains at least one defective item. In practice, the number d of defective items is often unknown in advance. In this paper, we present a new algorithm for the above group testing problem and prove that it has very good performance guarantee. More specifically, the number of tests used by the new algorithm is bounded from above by d log(n/d) + 3d + O(log²d). The new algorithm is designed based on a zig-zag approach that has not been studied before and is intuitive and easy to implement. When 0 < d < ρ₀n where ρ₀ = 1 − 4/e² = 0.45…, which holds for most practical applications, our new algorithm has better performance guarantee than any previous best result. Computational results show that the new algorithm has very good practical performances.