Deterministic M2M multicast in radio networks
Theoretical Computer Science
The identification of positive clones in a general inhibitor model
Journal of Computer and System Sciences
The wireless synchronization problem
Proceedings of the 28th ACM symposium on Principles of distributed computing
Noise-resilient group testing: limitations and constructions
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Competitive group testing and learning hidden vertex covers with minimum adaptivity
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Trusted computing for fault-prone wireless networks
DISC'10 Proceedings of the 24th international conference on Distributed computing
Superselectors: efficient constructions and applications
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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
Efficiently decodable error-correcting list disjunct matrices and applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Combinatorial group testing for corruption localizing hashing
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Analyzing graph structure via linear measurements
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On efficient gossiping in radio networks
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Adaptive phenotype testing for AND/OR items
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Randomized group testing both query-optimal and minimal adaptive
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
DISC'07 Proceedings of the 21st international conference on Distributed Computing
An extension of Stein-Lovász theorem and some of its applications
Journal of Combinatorial Optimization
Group testing with multiple mutually-obscuring positives
Information Theory, Combinatorics, and Search Theory
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Group testing refers to the situation in which one is given a set of objects ${\cal O}$, an unknown subset ${\cal P}\subseteq {\cal O}$, and the task of determining ${\cal P}$ by asking queries of the type "does ${\cal P}$ intersect $\cal Q$?," where $\cal Q$ is a subset of ${\cal O}$. Group testing is a basic search paradigm that occurs in a variety of situations such as quality control testing, searching in storage systems, multiple access communications, and data compression, among others. Group testing procedures have been recently applied in computational molecular biology, where they are used for screening libraries 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 ${\cal P}$, and an optimal algorithm for the case in which the outcome of tests may be unreliable because of the presence of "inhibitory" items in ${\cal O}$. Our results depend on a combinatorial structure introduced in this paper. We believe that it will prove useful in other contexts, too.