  The group testing problem consists of determining a small set of defective
items from a larger set of items based on a number of possibly-noisy tests, and
has numerous practical applications. One of the defining features of group
testing is whether the tests are adaptive (i.e., a given test can be chosen
based on all previous outcomes) or non-adaptive (i.e., all tests must be chosen
in advance). In this paper, building on the success of binary splitting
techniques in noiseless group testing (Hwang, 1972), we introduce noisy group
testing algorithms that apply noisy binary search as a subroutine. We provide
three variations of this approach with increasing complexity, culminating in an
algorithm that succeeds using a number of tests that matches the best known
previously (Scarlett, 2019), while overcoming fundamental practical limitations
of the existing approach, and more precisely capturing the dependence of the
number of tests on the error probability. We provide numerical experiments
demonstrating that adaptive group testing strategies based on noisy binary
search can be highly effective in practice, using significantly fewer tests
compared to state-of-the-art non-adaptive strategies.
