  We consider the group testing problem, in the case where the items are
defective independently but with non-constant probability. We introduce and
analyse an algorithm to solve this problem by grouping items together
appropriately. We give conditions under which the algorithm performs
essentially optimally in the sense of information-theoretic capacity. We use
concentration of measure results to bound the probability that this algorithm
requires many more tests than the expected number. This has applications to the
allocation of spectrum to cognitive radios, in the case where a database gives
prior information that a particular band will be occupied.
