Paper in proceedings, 2009

Suppose that we are given a set of n elements d of which are defective. A group test can check for any subset, called a pool, whether it contains a defective. It is well known that d defectives can be found by using O(d log n) pools. This nearly optimal number of pools can be achieved in 2 stages, where tests within a stage are done in parallel. But then d must be known in advance. Here we explore group testing strategies that use a nearly optimal number of pools and a few stages although d is not known to the searcher. One easily sees that O(log d) stages are sufficient for a strategy with O(d log n) pools. Here we prove a lower bound of O(log d/log log d) stages and a more general pools vs. stages tradeoff. As opposed to this, we devise a randomized strategy that finds d defectives using O(d log (n/d)) pools in 3 stages, with any desired probability. Open questions concern the optimal constant factors and practical
implications. A related problem motivated by, e.g., biological network analysis is to learn hidden vertex covers of a small size k in unknown graphs by edge group tests. (Does a given subset of vertices contain an edge?) We give a
1-stage strategy, with any FPT algorithm for vertex
cover enumeration as a decoder.

randomization

competitive group testing

nonadaptive strategy

adversary

vertex cover

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

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

03029743 (ISSN) 16113349 (eISSN)

Vol. 5699 84-95Computer Science

10.1007/978-3-642-03409-1_9

978-364203408-4