TY - JOUR

T1 - The Construction of Disjunct Matrix for Non-Adaptive Group Testing

AU - Zahidah, S.

AU - Barra, A.

N1 - Funding Information:
The authors are grateful to M I Utoyo and the reviewers for their suggestions and their comments. This work is supported by Faculty of Science and Technology, Universitas Airlangga.
Publisher Copyright:
© Published under licence by IOP Publishing Ltd.

PY - 2018/6/14

Y1 - 2018/6/14

N2 - Historically, group testing theory related to the testing of blood samples to identify a disease. Based on the algorithm, there are two types of group testing, Adaptive Group Testing (AGT) and Non-Adaptive Group Testing (NAGT). NAGT algorithm can be represented by a binary matrix M = mij, where columns are labeled by items and rows by tests (blocks). Criteria of matrix is m ij = 1 if test i contains item j and the other m ij = 0. On the other hand, the test results of each block are represented by a column vector, called outcome vector. Based on these representations, the problem of group testing can be viewed as finding representation matrix M which satisfies the equation Mx = y, where y is an outcome vector and x are tested samples. If there are d positive samples of n samples then we say d-Combinatorial Group Testing, abbreviated by d-CGT. This paper presents two constructions of disjunct matrix. The first construction based on generating of binary matrices and the second construction using modular equation. Furthermore, from the construction will be modified such that the new construction can be identified more than d positive samples.

AB - Historically, group testing theory related to the testing of blood samples to identify a disease. Based on the algorithm, there are two types of group testing, Adaptive Group Testing (AGT) and Non-Adaptive Group Testing (NAGT). NAGT algorithm can be represented by a binary matrix M = mij, where columns are labeled by items and rows by tests (blocks). Criteria of matrix is m ij = 1 if test i contains item j and the other m ij = 0. On the other hand, the test results of each block are represented by a column vector, called outcome vector. Based on these representations, the problem of group testing can be viewed as finding representation matrix M which satisfies the equation Mx = y, where y is an outcome vector and x are tested samples. If there are d positive samples of n samples then we say d-Combinatorial Group Testing, abbreviated by d-CGT. This paper presents two constructions of disjunct matrix. The first construction based on generating of binary matrices and the second construction using modular equation. Furthermore, from the construction will be modified such that the new construction can be identified more than d positive samples.

UR - http://www.scopus.com/inward/record.url?scp=85048868614&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1028/1/012116

DO - 10.1088/1742-6596/1028/1/012116

M3 - Conference article

AN - SCOPUS:85048868614

SN - 1742-6588

VL - 1028

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012116

T2 - 2nd International Conference on Statistics, Mathematics, Teaching, and Research 2017, ICSMTR 2017

Y2 - 9 October 2017 through 10 October 2017

ER -