Fig 4. Binary splitting by halving pooling example.

In this example, there are N = 96 samples and two of the samples are positive (red wells). To begin, all of the samples are pooled and tested (Step 1). If the first test is negative, testing is complete and all samples are considered negative. Otherwise, half of the samples are pooled and tested (Step 2). If the tested half is negative, then all of the samples in the tested half are considered to be negative and at least one positive sample is known to be present in the other non-tested half of the samples. If the tested half is positive, then it contains at least one positive sample and no information is gained about the other untested half. In either case, the method continues by halving and testing whichever group is known to contain a positive sample until a single positive sample is identified (either by individual testing, as seen in Step 7, or by elimination, as seen in Step 16). Once a single positive sample is identified, the remaining unresolved samples (non-grey wells) are pooled and tested to determine if any positive samples remain and the process continues until all positive samples are identified. Only one test is required per round, and in this example, it takes 17 sequential rounds to recover both positive samples.