Bounds for Nonadaptive Group Tests to Estimate the Amount of Defectives

The classical and well-studied group testing problem is to find d defectives in a set of n elements by group tests, which tell us for any chosen subset whether it contains defectives or not. Strategies are preferred that use both a small number of tests close to the informationtheoretic lower bound d log n, and a small constant number of stages, where tests in every stage are done in parallel, in order to save time. They should even work if d is completely unknown in advance. An essential ingredient of such competitive and minimal-adaptive group testing strategies is an estimate of d within a constant factor. More precisely, d shall be underestimated only with some given error probability, and overestimated only by a constant factor, called the competitive ratio. The latter problem is also interesting in its own right. It can be solved with O(log n) randomized group tests of a certain type. In this paper we prove that (log n) tests are really needed. The proof is based on an analysis o...

• Type: Journal
• Year: 2010
• Where: COCOA
• Authors: Peter Damaschke, Azam Sheikh Muhammad
• Keywords: COCOA 2010, Constant Factors, Discrete Geometry, Error Probability, Lower Bound