### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 42-56 |

Number of pages | 15 |

Journal | Journal of Computer and System Sciences |

Volume | 111 |

DOIs | |

State | Accepted/In press - Jan 1 2020 |

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### Keywords

- Deterministic algorithms
- Group testing
- Non-adaptive strategies
- Probabilistic method
- Threshold group testing

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Journal of Computer and System Sciences*,

*111*, 42-56. https://doi.org/10.1016/j.jcss.2020.02.002