Hong-Bin Chen

Nonadaptive algorithms for threshold group testing

Threshold group testing first proposed by Damaschke is a generalization of classic group testing. Specifically, a group test is positive (negative) if it contains at least u (at most l) positives, and if the number of positives is between l and u, the test outcome is arbitrary. Although sequential group testing algorithms have been proposed, it is unknown whether an efficient nonadaptive algorithm exists. In this paper, we give an affirmative answer to this problem by providing efficient nonadaptive algorithms for the threshold model. The key observation is that disjunct matrices, a standard tool for group testing designs, also work in this threshold model. This paper improves and extends previous results in three ways: 1. The algorithms we propose work in one stage, which saves time for testing. 2. The test complexity is lower than previous results, at least for the number of elements which need to be tested is sufficiently large. 3. A limited number of erroneous test outcomes are allowed.

A survey on nonadaptive group testing algorithms through the angle of decoding

Abstract Group testing, sometimes called pooling design, has been applied to a variety of problems such as blood testing, multiple access communication, coding theory, among others. Recently, screening experiments in molecular biology has become the most important application. In this paper, we review several models in this application by focusing on decoding, namely, giving a comparative study of how the problem is solved in each of these models.

Exploring the missing link among d-separable, d -separable and d-disjunct matrices

d-Disjunct matrices, d@?-separable matrices and d-separable matrices are well studied in various problems including group testing, coding, extremal set theory and, recently, DNA sequencing. The implications from the first two matrices to the last one are well documented. This paper gives an implication of the other direction for the first time.

An upper bound of the number of tests in pooling designs for the error-tolerant complex model

Recently pooling designs have been used in screening experiments in molecular biology. In some applications, the property to be screened is defined on subsets of items, instead of on individual items. Such a model is usually referred to as the complex model. In this paper we give an upper bound of the number of tests required in a pooling design for the complex model (with given design parameters) where experimental errors are allowed.

An unexpected meeting of four seemingly unrelated problems: graph testing, DNA complex screening, superimposed codes and secure key distribution

Abstract This paper discusses the relation among four problems: graph testing, DNA complex screening, superimposed codes and secure key distribution. We prove a surprising equivalence relation among these four problems, and use this equivalence to improve current results on graph testing. In the rest of this paper, we give a lower bound for the minimum number of tests on DNA complex screening model.

Reconstruction of hidden graphs and threshold group testing

AbstractClassical group testing is a search paradigm where the goal is the identification of individual positive elements in a large collection of elements by asking queries of the form “Does a set of elements contain a positive one?”. A graph reconstruction problem that generalizes the classical group testing problem is to reconstruct a hidden graph from a given family of graphs by asking queries of the form “Whether a set of vertices induces an edge”. Reconstruction problems on families of Hamiltonian cycles, matchings, stars and cliques on n vertices have been studied where algorithms of using at most 2nlg n,(1+o(1))(nlg n),2n and 2n queries were proposed, respectively. In this paper we improve them to

On Multicast Rearrangeable 3-stage Clos Networks Without First-Stage Fan-Out

(1+o(1))(n\lg n),(1+o(1))(\frac{n\lg n}{2}),n+2\lg n

An Almost Optimal Algorithm for Generalized Threshold Group Testing with Inhibitors

and n+lg n, respectively. Threshold group testing is another generalization of group testing which is to identify the individual positive elements in a collection of elements under a more general setting, in which there are two fixed thresholds ℓ and u, with ℓ<u, and the response to a query is positive if the tested subset of elements contains at least u positive elements, negative if it contains at most ℓ positive elements, and it is arbitrarily given otherwise. For the threshold group testing problem with ℓ=u−1, we show that p positive elements among n given elements can be determined by using O(plg n) queries, with a matching lower bound.

Group testing with multiple mutually-obscuring positives

For the multicast rearrangeable 3-stage Clos networks where input crossbars do not have fan-out capability, Kirkpatrick, Klawe, and Pippenger gave a sufficient condition and also a necessary condition which differs from the sufficient condition by a factor of 2. In this paper, we first tighten their conditions. Then we propose a new necessary condition based on the affine plane such that the necessary condition matches the sufficient condition for an infinite class of 3-stage Clos networks.

Are there more almost separable partitions than separable partitions

Group testing is a search paradigm where one is given a population S of n elements and an P is a subset of S defective elements and the goal is to determine P by performing tests on subsets of S. In classical group testing a test on a subset Q is a subset of S receives a YES response if [formula: see text] ≥ 1, and a NO response otherwise. In group testing with inhibitors (GTI), identifying the defective items is more difficult due to the presence of elements called inhibitors that interfere with the queries so that the answer to a query is YES if and only if the queried group contains at least one defective item and no inhibitor. In the present article, we consider a new generalization of the GTI model in which there are two unknown thresholds h and g and the response to a test is YES both in the case when the queried subset contains at least one defective item and less than h inhibitors, and in the case when the queried subset contains at least g defective items. Moreover, our search model assumes that no knowledge on the number |P| of defective items is given. We derive lower bounds on the minimum number of tests required to determine the defective items under this model and present an algorithm that uses an almost optimal number of tests.