Search problems
Key storage in secure networks
Discrete Applied Mathematics
Some new bounds for cover-free families
Journal of Combinatorial Theory Series A
Guessing secrets efficiently via list decoding
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Asymptotic Upper Bound for the Rate of (w, r) Cover-Free Codes
Problems of Information Transmission
Nonadaptive algorithms for threshold group testing
Discrete Applied Mathematics
Separating codes and a new combinatorial search model
Problems of Information Transmission
Improved constructions for non-daptive threshold group testing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Reconstruction of hidden graphs and threshold group testing
Journal of Combinatorial Optimization
General Theory of Information Transfer and Combinatorics
Nonrandom binary superimposed codes
IEEE Transactions on Information Theory
Finding one of D defective elements in some group testing models
Problems of Information Transmission
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We consider two generalizations of group testing: threshold group testing (introduced by Damaschke [11]) and majority group testing (a further generalization, including threshold group testing and a model introduced by Lebedev [20]). We show that each separating code gives a nonadaptive strategy for threshold group testing for some parameters. This is a generalization of a result in [4] on "guessing secrets", introduced in [9]. We introduce threshold codes and show that each threshold code gives a nonadaptive strategy for threshold group testing. Threshold codes include also the construction of [6]. In contrast to [8], where the number of defectives is bounded, we consider the case when the number of defectives are known. We show that we can improve the rate in this case. We consider majority group testing if the number of defective elements is unknown but bounded (otherwise it reduces to threshold group testing). We show that cover-free codes and separating codes give strategies for majority group testing. We give a lower bound for the rate of majority group testing.