Paper in proceedings, 2006

We introduce a natural generalization of the well-studied group testing problem: A test gives a positive (negative) answer if the pool contains at least u (at most l) positive elements, and an arbitrary answer if the number of positive elements is between these fixed thresholds l and u. We show that the p positive elements can be determined up to a constant number of misclassifications, bounded by the gap between the thresholds. This is in a sense the best
possible result. Then we study the number of tests needed
to achieve this goal if n elements are given. If the gap is zero, the complexity is, similarly to classical group testing, O(p log n) for any fixed u. For the general case
we propose a two-phase strategy consisting of a Distill and a Compress phase. We obtain some tradeoffs between classification accuracy and the number of tests.

combinatorial search

group testing

guessing secrets

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

Vol. 4123 707-718

Computer Science

978-3-540-46244-6