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# Testing Methods

We provide a short overview about the different testing methods that we apply for our comparison. All of these methods are either long established standard methods or are taken from peer reviewed journal articles.

### Indiviual Testing

Every person is tested individually.

### 2-level Pooling

1. All persons are distributed into pools of an optimal size
(with respect to the estimated infection rate). Samples of every person belonging to the same pool are tested jointly with one test.
2. If this initial test is negative, then the entire pool is disregarded as healthy. Else, every person in the pool is tested individually.

### Binary Splitting

1. All persons are distributed into pools of an optimal size (with respect to the estimated infection rate). Samples of every person belonging to the same pool are tested jointly with one test.
2. If the initial test is negative, then the entire pool is disregarded as healthy. Else, the pool is split into two pools of equal size.
3. For every new pool, this process is iterated recursively until pools of size one are reached or everybody is disregarded as healthy.

### Recursive Binary Splitting

1. A variation of binary splitting (see above).
2. If after a split of a pool into two pools and of equal size only one pool is tested positively, then one sick person is tracked down via splitting and continuing with the half of samples which surely contains at least one sick person. Potentially, a set of healthy persons is identified during the process of identifying a sick one.
3. The pools are redistributed: all persons, who have not been tested yet, are unified in one new joint pool, which is then tested.
4. The process is repeated recursively until every person is identified as sick or was disregarded as healthy in a negatively tested pool.

### Purim

1. All persons are distributed into pools of an optimal size (with respect to the estimated infection rate) of size k2. The k2 many person are labeled with a column and a row position between 1 and k.
2. All k persons belonging to the same column are pooled. Every one of these (k many) columns is tested in a pooled test.
3. The same process is repeated for the rows.
4. All persons whose row-test or column-test was negative are disregarded as healthy. Everybody else is tested individually.

### Sobel-R1

1. An approach relatively similar to recursive binary splitting (RBS - see above).
2. Main difference to RBS is that sizes of pools are optimized in every step of the hierarchy.
3. If one person is identified as sick, then, similar as in the case of RBS, the remaining persons are reshuffled into new pools.