论文标题
稀释（行学位）约束的最佳集合矩阵设计用于小组测试
Optimal Pooling Matrix Design for Group Testing with Dilution (Row Degree) Constraints
论文作者
论文摘要
在本文中，我们考虑了设计用于组测试的最佳合并矩阵的问题（例如，对于COVID-19病毒测试），其约束是可以将不超过$ r> 0 $样本汇总在一起，我们称之为“稀释约束”。这个问题转化为设计一个矩阵，其元素是每行不超过$ r $'1的元素，并且具有识别异常元素的一定性能保证。我们明确地提供了满足稀释限制并具有识别异常元素的性能保证的合并矩阵设计，并证明了它们在节省最大测试中的最佳性，而不是表明该设计的矩阵具有最大的宽度宽度比率。
In this paper, we consider the problem of designing optimal pooling matrix for group testing (for example, for COVID-19 virus testing) with the constraint that no more than $r>0$ samples can be pooled together, which we call "dilution constraint". This problem translates to designing a matrix with elements being either 0 or 1 that has no more than $r$ '1's in each row and has a certain performance guarantee of identifying anomalous elements. We explicitly give pooling matrix designs that satisfy the dilution constraint and have performance guarantees of identifying anomalous elements, and prove their optimality in saving the largest number of tests, namely showing that the designed matrices have the largest width-to-height ratio among all constraint-satisfying 0-1 matrices.
