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We consider the quantitative group testing problem where the objective is toidentify defective items in a given population based on results of testsperformed on subsets of the population. Under the quantitative group testingmodel, the result of each test reveals the number of defective items in thetested group. The minimum number of tests achievable by nested test plans wasestablished by Aigner and Schughart in 1985 within a minimax framework. Theoptimal nested test plan offering this performance, however, was not obtained.In this work, we establish the optimal nested test plan in closed form. Thisoptimal nested test plan is also order optimal among all test plans as thepopulation size approaches infinity. Using heavy-hitter detection as a casestudy, we show via simulation examples orders of magnitude improvement of thegroup testing approach over two prevailing sampling-based approaches indetection accuracy and counter consumption. Other applications include anomalydetection and wideband spectrum sensing in cognitive radio systems.

Optimal Nested Test Plan for Combinatorial Quantitative Group Testing