Combinatorial search
Reconstructing a Hamiltonian cycle by querying the graph: application to DNA physical mapping
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Some new bounds for cover-free families
Journal of Combinatorial Theory Series A
An optimal procedure for gap closing in whole genome shotgun sequencing
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
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
Nonrandom binary superimposed codes
IEEE Transactions on Information Theory
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
Threshold and majority group testing
Information Theory, Combinatorics, and Search Theory
Superimposed codes and threshold group testing
Information Theory, Combinatorics, and Search Theory
Group testing with multiple mutually-obscuring positives
Information Theory, Combinatorics, and Search Theory
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Threshold group testing first proposed by Damaschke is a generalization of classic group testing. Specifically, a group test is positive (negative) if it contains at least u (at most l) positives, and if the number of positives is between l and u, the test outcome is arbitrary. Although sequential group testing algorithms have been proposed, it is unknown whether an efficient nonadaptive algorithm exists. In this paper, we give an affirmative answer to this problem by providing efficient nonadaptive algorithms for the threshold model. The key observation is that disjunct matrices, a standard tool for group testing designs, also work in this threshold model. This paper improves and extends previous results in three ways: 1. The algorithms we propose work in one stage, which saves time for testing. 2. The test complexity is lower than previous results, at least for the number of elements which need to be tested is sufficiently large. 3. A limited number of erroneous test outcomes are allowed.