A new competitive algorithm for group testing

Abstract

Algorithms for the group testing problem when there is no a priori information on the number of defective items are considered. The efficiency criterion used is the competitive ratio, which is the ratio of the number of tests required by an algorithm when there is no a priori information on the number of defective items, to the number of tests required by an optimal algorithm when the number of defective items is known in advance. A new algorithm is presented, and it is shown that the competitive ratio of this algorithm is 2. This result is an improvement over a previous algorithm due to Du and Hwang (1990) the competitive ratio of which is 2.75. It also proves a conjecture made by Du and Hwang. A new application of group testing techniques for high-speed network is discussed. © 1994.