A Variation of Cover-Free Families and Its Applications.

A cover-free family is a family of subsets of a finite set in which no one is covered by the union of r others. We study a variation of cover-free family: A binary matrix is ( r, w] -consecutive-disjunct if for any w cyclically consecutive columns and another r cyclically consecutive columns , there exists one row intersecting but none of . In group testing, the goal is to determine a small subset of positive items D in a large population by group tests. By applying consecutive-disjunct matrices, we solve threshold group testing of consecutive positives in group tests nonadaptively, and the decoding complexity is where u is a threshold parameter in threshold group testing and it is assumed that | D|≤ d and . Meanwhile, we obtain that for group testing of consecutive positives, all positives can be identified in group tests nonadaptively and the decoding complexity is . [ABSTRACT FROM AUTHOR]