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 -