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
An optimal procedure for gap closing in whole genome shotgun sequencing
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
The Journal of Machine Learning Research
Learning a hidden graph using O( logn) queries per edge
Journal of Computer and System Sciences
Nonadaptive algorithms for threshold group testing
Discrete Applied 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
General Theory of Information Transfer and Combinatorics
Improved constructions for non-daptive threshold group testing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Threshold and majority 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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Classical group testing is a search paradigm where the goal is the identification of individual positive elements in a large collection of elements by asking queries of the form "Does a set of elements contain a positive one?". A graph reconstruction problem that generalizes the classical group testing problem is to reconstruct a hidden graph from a given family of graphs by asking queries of the form "Whether a set of vertices induces an edge". Reconstruction problems on families of Hamiltonian cycles, matchings, stars and cliques on n vertices have been studied where algorithms of using at most 2nlg驴n,(1+o(1))(nlg驴n),2n and 2n queries were proposed, respectively. In this paper we improve them to $(1+o(1))(n\lg n),(1+o(1))(\frac{n\lg n}{2}),n+2\lg n$ and n+lg驴n, respectively. Threshold group testing is another generalization of group testing which is to identify the individual positive elements in a collection of elements under a more general setting, in which there are two fixed thresholds 驴 and u, with 驴u, and the response to a query is positive if the tested subset of elements contains at least u positive elements, negative if it contains at most 驴 positive elements, and it is arbitrarily given otherwise. For the threshold group testing problem with 驴=u驴1, we show that p positive elements among n given elements can be determined by using O(plg驴n) queries, with a matching lower bound.