### Abstract

The task of non-adaptive group testing is to identify up to d defective items from N items, where a test is positive if it contains at least one defective item, and negative otherwise. If there are t tests, they can be represented as a t × N measurement matrix. We have answered the question of whether there exists a scheme such that a larger measurement matrix, built from a given t × N measurement matrix, can be used to identify up to d defective items in) time O(t log
_{2}
N). In the meantime, a t × N nonrandom measurement matrix with (forumala presented). can be obtained to identify up to d defective items in time poly(t). This is much better than the
^{2}
best
^{2}
well-known
^{2 2}
bound,
^{2}
t = O (d
^{2}
log
^{2}
_{2}
N. For the special case d = 2, there exists an efficient nonrandom construction in which at most two defective items can be identified in time 4 log
^{2}
_{2}
N using t = 4 log
^{2}
_{2}
N tests. Numerical results show that our proposed scheme is more practical than existing ones, and experimental results confirm our theoretical analysis. In particular, up to 2
^{7}
= 128 defective items can be identified in less than 16 s even for N = 2
^{100}
.

Original language | English |
---|---|

Pages (from-to) | 245-256 |

Number of pages | 12 |

Journal | Journal of Information Processing |

Volume | 27 |

DOIs | |

Publication status | Published - Jan 1 2019 |

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### Keywords

- Combinatorics
- Efficient decoding
- Non-adaptive group testing
- Nonrandom construction

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Journal of Information Processing*,

*27*, 245-256. https://doi.org/10.2197/ipsjjip.27.245