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FCT
2009
Springer

Competitive Group Testing and Learning Hidden Vertex Covers with Minimum Adaptivity

9 years 10 months ago
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., ...
Peter Damaschke, Azam Sheikh Muhammad
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where FCT
Authors Peter Damaschke, Azam Sheikh Muhammad
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