Consecutive positive detectable matrices and group testing for consecutive positives
Consecutive positive detectable matrices and group testing for consecutive positives
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DOI：
10.1016/s0012-365x(03)00282-6
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发表时间：
2004-03-28
影响因子：
0.8
通讯作者：
Jimbo, M
中科院分区：
文献类型：
--
作者：
M端ller, M;Jimbo, M
科尔本(Ann.康宁。3(1999)37-41)发展了一些非适应性团体测验的策略，当项目是线性排序的，并且肯定项目构成所有项目的连续子集时。我们通过引入2-连续正检测矩阵(2CPD-矩阵)的概念来改进他的策略，该概念要求所有列和每两个连续列的逐位或和是成对不同的。如果这样的矩阵相对于某些明显的约束具有最大可能列数，则称其为极大。利用递归结构，证明了除m=3外，对于任意列m，极大2CPD-矩阵的存在性都是N的元素。此外，我们还构造了极大2CPD-矩阵，其中每一列都具有一定的恒定权重。这导致了池化设计，其中每个项目出现在相同数量的池中，并且所有池的大小相同。(C)2003爱思唯尔B.V.保留所有权利。
Colbourn (Ann. Combin. 3 (1999) 37-41) developed some strategy for nonadaptive group testing when the items are linearly ordered and the positives items form a consecutive subset of all items. We improve his strategy by introducing the concept of 2-consecutive positive detectable matrices (2CPD-matrix) requiring that all columns and bitwise OR-sum of each two consecutive columns are pairwise distinct. Such a matrix is called maximal if it has a maximal possible number of columns with respect to some obvious constraints. Using a recursive construction we prove the existence of maximal 2CPD-matrices for any column size m is an element of N except for the case m = 3. Furthermore, we construct maximal 2CPD-matrices where each column is of some fixed constant weight. This leads to pooling designs, where each item appears in the same number of pools and all pools are of the same size. (C) 2003 Elsevier B.V. All rights reserved.