Competitive Group Testing and Learning Hidden Vertex Covers with Minimum Adaptivity

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 Ω(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 1 − . Open questions concern the optimal constant factors and practical implications. A related problem motivated by, e.g., ...

• Type: Conference
• Year: 2009
• Where: FCT
• Authors: Peter Damaschke, Azam Sheikh Muhammad
• Keywords: FCT 2009, Group Test, Group Testing, Log N, Theoretical Computer Science