Group testing concerns itself with the accurate recovery of a set of "defective" items from a larger population via a series of tests. While most works in this area have considered the classical group testing model, where tests are binary and indicate the presence of at least one defective item in the test, we study the cascaded group testing model. In cascaded group testing, tests admit an ordering, and test outcomes indicate the first defective item in the test under this ordering. Under this model, we establish various achievability bounds for several different recovery criteria using both non-adaptive and adaptive (with "few" stages) test designs.

翻译：群组测试旨在通过一系列测试从较大群体中准确恢复一组“缺陷”物品。虽然该领域的大多数研究都考虑了经典的群组测试模型（其中测试结果为二元值，仅指示测试中是否存在至少一个缺陷物品），但本文研究了级联群组测试模型。在级联群组测试中，测试允许存在顺序，且测试结果指示该顺序下测试中首个出现的缺陷物品。在此模型下，我们通过非自适应和自适应（使用“少量”阶段）测试设计，针对多种不同的恢复准则建立了多种可达性界。