Competitive group testing and learning hidden vertex covers with minimum adaptivity
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

Author

Peter Damaschke

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

Muhammad Azam Sheikh

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

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 5699 84-95

Subject Categories

Computer Science

DOI

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

ISBN

978-364203408-4

More information

Created

10/6/2017