The screening of data sets is essential to modern technology. Whenever the objective is to find "positive elements" in a data set, a test indicating whether at least one positive is an element of a specific part of the data set can greatly facilitate their isolation. Such tests are called binary group tests and the general mathematical method behind the identification of the positives using such tests is known as classical group testing. In many applied settings, the use of classical group testing to isolate objects that are individually positive has become standard experimental procedure. However, very little work has been done in applying group testing techniques to the identification of objects that are collectively positive. Let C be an unknown collection of subsets or complexes in a population and let P be a pool taken from the population. A pool P is said to be positive if and only if a member of C is also a subset of P. The identification of C by the application of these binary tests is called group testing for complexes.
The primary aim of this proposal is the development of efficient group testing methods that lead to the identification of positive combinations of objects, namely the positive complexes. There are many scientific and technical areas where the identification of positive combinations of objects is important. Computationally feasible methods of finding combinations of entities that produce some measurable outcome or are measurably linked to some function or disfunction would have important applications to medical genetics, computer security, software testing, data mining, communications, and marketing.
