  The goal of combinatorial group testing is to efficiently identify up to $d$
defective items in a large population of $n$ items, where $d \ll n$. Defective
items satisfy certain properties while the remaining items in the population do
not. To efficiently identify defective items, a subset of items is pooled and
then tested. In this work, we consider complex group testing (CmplxGT) in which
a set of defective items consists of subsets of positive items (called
\textit{positive complexes}). CmplxGT is classified into two categories:
classical CmplxGT (CCmplxGT) and generalized CmplxGT (GCmplxGT). In CCmplxGT,
the outcome of a test on a subset of items is positive if the subset contains
at least one positive complex, and negative otherwise. In GCmplxGT, the outcome
of a test on a subset of items is positive if the subset has a certain number
of items of some positive complex, and negative otherwise.
  For CCmplxGT, we present a scheme that efficiently identifies all positive
complexes in time $t \times \mathrm{poly}(d, \ln{n})$ in the presence of
erroneous outcomes, where $t$ is a predefined parameter. As $d \ll n$, this is
significantly better than the currently best time of $\mathrm{poly}(t) \times
O(n \ln{n})$. Moreover, in specific cases, the number of tests in our proposed
scheme is smaller than previous work. For GCmplxGT, we present a scheme that
efficiently identifies all positive complexes. These schemes are directly
applicable in various areas such as complex disease genetics, molecular
biology, and learning a hidden graph.
