Paper in proceedings, 2010

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 information-theoretic 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 O(log n) tests are really needed. The proof is based on an analysis of the influence of tests on the searcher's ability to distinguish between any two candidate numbers with a constant ratio. Once we know this lower bound, the next challenge is to get optimal constant factors in the O(log n) test number, depending on the desired error probability and competitive ratio. We give a method to derive upper bounds and conjecture that our particular strategy is already optimal.

learning by queries

lower bound

algorithm

competitive group testing

randomized strategy

nonadaptive strategy

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

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

03029743 (ISSN) 16113349 (eISSN)

Vol. 6509 PART 2 117-130Information and Communication Technology

Life Science Engineering (2010-2018)

Basic sciences

Computer Science

10.1007/978-3-642-17461-2_10

978-3-642-17460-5