Adaptive group testing with a constrained number of positive responses improved
Journal article, 2016

Group testing aims at identifying the defective elements of a set by testing selected subsets called pools. A test gives a positive response if the tested pool contains some defective elements. Adaptive strategies test the pools one by one. Assuming that only a tiny minority of elements are defective, the main objective of group testing strategies is to minimize the number of tests. De Bonis introduced in COCOA 2014 a problem variant where one also wants to limit the number of positive tests, as they have undesirable side effects in some applications. A strategy was given with asymptotically optimal test complexity, subject to a constant factor. In the present paper we reduce the test complexity, making also the constant factor optimal in the limit. This is accomplished by a routine that searches for a single defective element and uses pools of decreasing sizes even after negative responses. An additional observation is that randomization saves a further considerable fraction of tests compared to the deterministic worst case, if the number of permitted positive responses per defective element is small.

randomized strategy

adaptive strategy

group testing

positive test


Peter Damaschke

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Discrete Applied Mathematics

0166-218X (ISSN)

Vol. 205 208-212


Basic sciences

Subject Categories

Discrete Mathematics



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