Modifications of Competitive Group Testing
SIAM Journal on Computing
A new competitive algorithm for group testing
Discrete Applied Mathematics
SIAM Journal on Computing
On parallel attribute-efficient learning
Journal of Computer and System Sciences
Improved Results for Competitive Group Testing
Combinatorics, Probability and Computing
SIAM Journal on Discrete Mathematics
Optimal Two-Stage Algorithms for Group Testing Problems
SIAM Journal on Computing
Parameterized enumeration, transversals, and imperfect phylogeny reconstruction
Theoretical Computer Science - Parameterized and exact computation
Improved Combinatorial Group Testing Algorithms for Real-World Problem Sizes
SIAM Journal on Computing
Learning a hidden graph using O( logn) queries per edge
Journal of Computer and System Sciences
Combinatorial search on graphs motivated by bioinformatics applications: a brief survey
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
New and improved BIST diagnosis methods from combinatorial Group testing theory
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Bounds for nonadaptive group tests to estimate the amount of defectives
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Synthetic sequence design for signal location search
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
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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 - Ɛ. 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 using O(k3 log n) pools, with any FPT algorithm for vertex cover enumeration as a decoder.