Adaptive Phenotype Testing for AND/OR Items

The combinatorial group testing problem is concerned with the design of experiments so as to minimize the number of tests needed to find the sets of items responsible for a particular phenotype (an observable property). The traditional group testing problem only considers the OR problem, i.e. the phenotype appears as long as one of the responsible items exists. In this paper, we introduce the phenotype testing problem which is a generalization of the well-studied combinatorial group testing problem. In practice, there are more than one phenotype and the responsible items and their mechanism (AND or OR) for each phenotype are unknown where an AND mechanism means that the phenotype only appears if all of the responsible items exist.

This phenotype testing problem has an important application in biological research, known as phenotype knockout study. New algorithms for designing adaptive experiments for solving the phenotype testing problem with

n

items using

O

(log

n

) tests in the worst cases are introduced. When the number of phenotypes is small, say at most 2, and the number of responsible items for each phenotype is at most 2, algorithms with near-optimal number of tests are presented.