Title : Group Testing Designs : A Combinatorial Marvel Speaker: Bikas K Sinha Retired Professor of Statistics Indian Statistical Institute, Kolkata Abstract : Group Testing is a technique to test a collection of units in several groups, rather than in isolation (i.e., one-at-a-time), in order to ascertain the 'status' of each individual unit in the collection in respect of a well-defined 'feature'. The problem is to plan the testing procedure so as to be able to do so without any ambiguity and with a minimum number of such tests [called Group Tests (GTs)]. The response to be extracted from each unit is on the same 'feature' and it is 'binary' in nature. It is tacitly assumed that 'possession' of the feature by at least one unit within a group [so formed] would render the group 'identifiable' as 'possessed'. When this happens, we need to 'open up' the group and go for further exploration of the status of individual units of the group, possibly by sub-group(s) testing or by other means. Other possibility is that the group would be declared as 'passed', and consequently, it would mean that all constituent units within the group would be declared as 'passed' and 'at one go'! This interpretation is accepted for Group Testing schemes to work. When this latter phenomenon happens, the merit of Group Testing prevails over testing individual units in terms of reduction in the required number of tests. For a given collection of units, we may adopt one-at-a-time testing or Group Testing with formation of suitable groups, or even a combination of the two strategies. As is mentioned above, the sole purpose is to minimize the number of GTs in such situations for a given collection of test items. The above formulation looks deceptively simple! Hidden are probabilistic and combinatorial challenges. In this talk, we will discuss some issues related to combinatorial challenges only. Key Words.... Group tests; Hypergeometric group tests, Sequential group tests, t-completeness, Detecting power of order t, Group Divisible Designs, Petersen graphs.