Efficient (Nonrandom) construction and decoding for non-adaptive group testing

Thach V. Bui, Minoru Kuribayashi, Tetsuya Kojima, Roghayyeh Haghvirdinezhad, Isao Echizen

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)245-256
Number of pages12
JournalJournal of Information Processing
Volume27
DOIs
Publication statusPublished - Jan 1 2019

Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)

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