TY - JOUR
T1 - Subquadratic non-adaptive threshold group testing
AU - De Marco, Gianluca
AU - Jurdziński, Tomasz
AU - Kowalski, Dariusz R.
AU - Różański, Michał
AU - Stachowiak, Grzegorz
N1 - Funding Information:
This work was supported by the Polish National Science Centre grants DEC-2012/06/M/ST6/00459 and 2014/13/N/ST6/01850.
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/8
Y1 - 2020/8
N2 - We consider threshold group testing – a generalization of group testing, which asks to identify a set of positive individuals in a population, by performing tests on pools of elements. Each test is represented by a subset Q of individuals and its output is yes if Q contains at least one positive element and no otherwise. Threshold group testing is the natural generalization, introduced by P. Damaschke in 2005, arising when we are given a threshold t>0 and the answer to a test Q is yes if Q contains at least t positives and no otherwise. We give upper and lower bounds for this general problem, showing a complexity separation with the classical group testing. Next, we introduce a further generalization in which the goal is minimizing not only the number of tests, but also the number of thresholds which is related to the accuracy of the tests.
AB - We consider threshold group testing – a generalization of group testing, which asks to identify a set of positive individuals in a population, by performing tests on pools of elements. Each test is represented by a subset Q of individuals and its output is yes if Q contains at least one positive element and no otherwise. Threshold group testing is the natural generalization, introduced by P. Damaschke in 2005, arising when we are given a threshold t>0 and the answer to a test Q is yes if Q contains at least t positives and no otherwise. We give upper and lower bounds for this general problem, showing a complexity separation with the classical group testing. Next, we introduce a further generalization in which the goal is minimizing not only the number of tests, but also the number of thresholds which is related to the accuracy of the tests.
KW - Deterministic algorithms
KW - Group testing
KW - Non-adaptive strategies
KW - Probabilistic method
KW - Threshold group testing
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U2 - 10.1016/j.jcss.2020.02.002
DO - 10.1016/j.jcss.2020.02.002
M3 - Article
AN - SCOPUS:85079903039
VL - 111
SP - 42
EP - 56
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
SN - 0022-0000
ER -