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The Construction of Disjunct Matrix for Non-Adaptive Group Testing
Zahidah S.a, Barra A.b
a Department of Mathematics, Universitas Airlangga, Surabaya, 60115, Indonesia
b Department of Mathematics, Institut Teknologi Bandung, Bandung, 40132, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© Published under licence by IOP Publishing Ltd.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.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]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.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1088/1742-6596/1028/1/012116[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]