Group Testing with Multiple Inhibitor Sets and Error-Tolerant and Its Decoding Algorithms.

In this article, we advance a new group testing model [Formula: see text] with multiple inhibitor sets and error-tolerant and propose decoding algorithms for it to identify all its positives by using [Formula: see text]-disjunct matrix. The decoding complexity for it is [Formula: see text], where [Formula: see text]. Moreover, we extend this new group testing to threshold group testing and give the threshold group testing model [Formula: see text] with multiple inhibitor sets and error-tolerant. By using [Formula: see text]-disjunct matrix, we propose its decoding algorithms for gap g = 0 and g > 0, respectively. Finally, we point out that the new group testing is the natural generalization for the clone model.

Nonadaptive algorithms for threshold group testing with inhibitors and error-tolerance.

A group test gives a positive (negative) outcome if it contains at least u (at most l) positive items, and an arbitrary outcome if the number of positive items is between thresholds l and u. This problem introduced by Damaschke is called threshold group testing. It is a generalization of classical group testing. Chen and Fu extended this problem to the error-tolerant version and first proposed efficient nonadaptive algorithms. In this article, we extend threshold group testing to the k-inhibitors model in which a test has a positive outcome if it contains at least u positives and at most k-1 inhibitors. By using (d + k - l, u; 2e + 1]-disjunct matrix we provide nonadaptive algorithms for the threshold group testing model with k-inhibitors and at most e-erroneous outcomes. The decoding complexity is O(n(u+k) log n) for fixed parameters (d, u, l, k, e).

Efficient error-correcting pooling designs constructed from pseudo-symplectic spaces over a finite field.

In this article, we construct two classes of t × n, s(e)-disjunct matrix with subspaces in pseudo-symplectic space F(q)(²v +¹) of characteristic 2 and prove that the test efficiency t/n of these constructions are smaller than that of D'yachkov et al. (2005).

New algebraic constructions for pooling design in DNA library screening.

Pooling design is an important mathematical tool in DNA library screening. It has been showed that using pooling design, the number of tests in DNA library screening can be greatly reduced. In this paper, we present some new algebraic constructions for pooling design.