A tractable non-adaptative group testing method for non-binary measurements

The original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least one defective element in the group. The aim is then to identify all defective items of the collection with as few tests as possible. This problem is relevant in several fields, among which biology and computer sciences. In the present article we consider that the tests applied to groups of items returns a load , measuring how defective the most defective item of the group is. In this setting, we propose a simple non-adaptative algorithm allowing the detection of all defective items of the collection. Items are put on an n×n grid and pools are organised as lines, columns and diagonals of this grid. This method improves on classical group testing algorithms using only the binary response of the test.