  In the group-testing literature, efficient algorithms have been developed to
minimize the number of tests required to identify all minimal "defective"
sub-groups embedded within a larger group, using deterministic group splitting
with a generalized binary search. In a separate literature, researchers have
used a stochastic group splitting approach to efficiently sample from the
intractable number of minimal defective sets of outages in electrical power
systems that trigger large cascading failures, a problem in which positive
tests can be much more computationally costly than negative tests. In this
work, we generate test problems with variable numbers of defective sets and a
tunable positive:negative test cost ratio to compare the efficiency of
deterministic and stochastic adaptive group splitting algorithms for
identifying defective edges in hypergraphs. For both algorithms, we show that
the optimal initial group size is a function of both the prevalence of
defective sets and the positive:negative test cost ratio. We find that
deterministic splitting requires fewer total tests but stochastic splitting
requires fewer positive tests, such that the relative efficiency of these two
approaches depends on the positive:negative test cost ratio. We discuss some
real-world applications where each of these algorithms is expected to
outperform the other.
