  Group testing enables to identify infected individuals in a population using
a smaller number of tests than individual testing. To achieve this, group
testing algorithms commonly assume knowledge of the number of infected
individuals; nonadaptive and several adaptive algorithms fall in this category.
Some adaptive algorithms, like binary splitting, operate without this
assumption, but require a number of stages that may scale linearly with the
size of the population. In this paper we contribute a new algorithm that
enables a balance between the number of tests and the number of stages used,
and which we term diagonal group testing. Diagonal group testing, like binary
splitting, does not require knowledge of the number of infected individuals,
yet unlike binary splitting, is order-optimal w.r.t. the expected number of
tests it requires and is guaranteed to succeed in a small number of stages that
scales at most logarithmically with the size of the population. Numerical
evaluations, for diagonal group testing and a hybrid approach we propose,
support our theoretical findings.
