### Abstract

Identification of up to d defective items and up to h inhibitors in a set of n items is the main task of non-adaptive group testing with inhibitors. To reduce the cost of this Herculean task, a subset of the n items is formed and then tested. This is called group testing. A test outcome on a subset of items is positive if the subset contains at least one defective item and no inhibitors, and negative otherwise. We present two decoding schemes for efficiently identifying the defective items and the inhibitors in the presence of e erroneous outcomes in time poly(d, h, e, log
_{2}
n>, which is sublinear to the number of items. This decoding complexity significantly improves the state-of-the-art schemes in which the decoding time is linear to the number of items, i.e., poly(d,h,e,n). Moreover, each column of the measurement matrices associated with the proposed schemes can be nonrandomly generated in polynomial order of the number of rows. As a result, one can save space for storing them. Simulation results confirm our theoretical analysis. When the number of items is sufficiently large, the decoding time in our proposed scheme is smallest in comparison with existing work. In addition, when some erroneous outcomes are allowed, the number of tests in the proposed scheme is often smaller than the number of tests in existing work.

Original language | English |
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Title of host publication | Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings |

Editors | T. V. Gopal, Junzo Watada |

Publisher | Springer Verlag |

Pages | 93-113 |

Number of pages | 21 |

ISBN (Print) | 9783030148119 |

DOIs | |

Publication status | Published - Jan 1 2019 |

Event | 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019 - Kitakyushu, Japan Duration: Apr 13 2019 → Apr 16 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 11436 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019 |
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Country | Japan |

City | Kitakyushu |

Period | 4/13/19 → 4/16/19 |

### Fingerprint

### Keywords

- Non-adaptive group testing
- Sparse recovery
- Sublinear algorithm

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings*(pp. 93-113). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11436 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-14812-6_7

**Sublinear decoding schemes for non-adaptive group testing with inhibitors.** / Bui, Thach V.; Kuribayashi, Minoru; Kojima, Tetsuya; Echizen, Isao.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11436 LNCS, Springer Verlag, pp. 93-113, 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019, Kitakyushu, Japan, 4/13/19. https://doi.org/10.1007/978-3-030-14812-6_7

}

TY - GEN

T1 - Sublinear decoding schemes for non-adaptive group testing with inhibitors

AU - Bui, Thach V.

AU - Kuribayashi, Minoru

AU - Kojima, Tetsuya

AU - Echizen, Isao

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Identification of up to d defective items and up to h inhibitors in a set of n items is the main task of non-adaptive group testing with inhibitors. To reduce the cost of this Herculean task, a subset of the n items is formed and then tested. This is called group testing. A test outcome on a subset of items is positive if the subset contains at least one defective item and no inhibitors, and negative otherwise. We present two decoding schemes for efficiently identifying the defective items and the inhibitors in the presence of e erroneous outcomes in time poly(d, h, e, log 2 n>, which is sublinear to the number of items. This decoding complexity significantly improves the state-of-the-art schemes in which the decoding time is linear to the number of items, i.e., poly(d,h,e,n). Moreover, each column of the measurement matrices associated with the proposed schemes can be nonrandomly generated in polynomial order of the number of rows. As a result, one can save space for storing them. Simulation results confirm our theoretical analysis. When the number of items is sufficiently large, the decoding time in our proposed scheme is smallest in comparison with existing work. In addition, when some erroneous outcomes are allowed, the number of tests in the proposed scheme is often smaller than the number of tests in existing work.

AB - Identification of up to d defective items and up to h inhibitors in a set of n items is the main task of non-adaptive group testing with inhibitors. To reduce the cost of this Herculean task, a subset of the n items is formed and then tested. This is called group testing. A test outcome on a subset of items is positive if the subset contains at least one defective item and no inhibitors, and negative otherwise. We present two decoding schemes for efficiently identifying the defective items and the inhibitors in the presence of e erroneous outcomes in time poly(d, h, e, log 2 n>, which is sublinear to the number of items. This decoding complexity significantly improves the state-of-the-art schemes in which the decoding time is linear to the number of items, i.e., poly(d,h,e,n). Moreover, each column of the measurement matrices associated with the proposed schemes can be nonrandomly generated in polynomial order of the number of rows. As a result, one can save space for storing them. Simulation results confirm our theoretical analysis. When the number of items is sufficiently large, the decoding time in our proposed scheme is smallest in comparison with existing work. In addition, when some erroneous outcomes are allowed, the number of tests in the proposed scheme is often smaller than the number of tests in existing work.

KW - Non-adaptive group testing

KW - Sparse recovery

KW - Sublinear algorithm

UR - http://www.scopus.com/inward/record.url?scp=85064866979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064866979&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-14812-6_7

DO - 10.1007/978-3-030-14812-6_7

M3 - Conference contribution

SN - 9783030148119

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 93

EP - 113

BT - Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings

A2 - Gopal, T. V.

A2 - Watada, Junzo

PB - Springer Verlag

ER -