Correction to "An asymptotically nonadaptive algorithm for conflict resolution i
IEEE Transactions on Information Theory
Search problems
Combinatorial search
Locality in distributed graph algorithms
SIAM Journal on Computing
On the upper bound of the size of the r-cover-free families
Journal of Combinatorial Theory Series A
Randomized algorithms
Journal of Combinatorial Theory Series A
Deterministic restrictions in circuit complexity
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The AETG System: An Approach to Testing Based on Combinatorial Design
IEEE Transactions on Software Engineering
Adaptive versus nonadaptive attribute-efficient learning
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Randomized group testing for mutually obscuring defectives
Information Processing Letters
Improved algorithms for group testing with inhibitors
Information Processing Letters
Lower bounds for identifying subset members with subset queries
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Selective families, superimposed codes, and broadcasting on unknown radio networks
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Explicit constructions of selectors and related combinatorial structures, with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Machine Learning
Machine Learning
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Group Testing for Image Compression
DCC '00 Proceedings of the Conference on Data Compression
Reconstructing strings from substrings in rounds
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Deterministic Superimposed Coding with Applications to Pattern Matching
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Fast broadcasting and gossiping in radio networks
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Group Testing Problems with Sequences in Experimental Molecular Biology
SEQUENCES '97 Proceedings of the Compression and Complexity of Sequences 1997
Application of cover-free codes and combinatorial designs to two-stage testing
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Asymptotic efficiency of two-stage disjunctive testing
IEEE Transactions on Information Theory
On selection problem in radio networks
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Efficient parallel algorithms for dead sensor diagnosis and multiple access channels
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
International Journal of Bioinformatics Research and Applications
Centralized Communication in Radio Networks with Strong Interference
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Information Processing Letters
Deterministic communication in the weak sensor model
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Deterministic recurrent communication and synchronization in restricted sensor networks
ALGOSENSORS'10 Proceedings of the 6th international conference on Algorithms for sensor systems, wireless adhoc networks, and autonomous mobile entities
Average-Time complexity of gossiping in radio networks
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Deterministic recurrent communication in restricted Sensor Networks
Theoretical Computer Science
Improved combinatorial group testing for real-world problem sizes
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Almost optimal explicit selectors
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
General Theory of Information Transfer and Combinatorics
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Efficient symmetry breaking in multi-channel radio networks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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Group Testing refers to the situation in which one is given a set of objects O, an unknown subset P ⊆ O, and the task is to determine P by asking queries of the type "does P intersect Q?", where Q is a subset of O. Group testing is a basic search paradigm that occurs in a variety of situations such as quality control in product testing, searching in storage systems, multiple access communications, and software testing, among the others. Group testing procedures have been recently applied in Computational Molecular Biology, where they are used for screening library of clones with hybridization probes and sequencing by hybridization. Motivated by particular features of group testing algorithms used in biological screening, we study the efficiency of two-stage group testing procedures. Our main result is the first optimal two-stage algorithm that uses a number of tests of the same order as the information theoretic lower bound on the problem. We also provide efficient algorithms for the case in which there is a Bernoulli probability distribution on the possible sets P, and an optimal algorithm for the case in which the outcome of tests may be unreliable because of the presence of "inhibitory" items in O. Our results depend on a combinatorial structure introduced in this paper. We believe that it will prove useful in other contexts too.