Some Classes Of Pooling Designs And Error-correcting Properties

A pooling design based on clone library screenings is an experimental strategyto find clones which contain special nucleotide strings; it is also an algorithm ofcombinatorial group testing. Now the pooling design is widely used in the exami-nation of low incidence. For example, Biology experiments, Medicine(such as DNATesting)and so on.A pooling design is usually represented by a binary matrix M(also called adisjunct matrix), whose rows correspond to pools and columns correspond to clones.The elements of M are only1or0. Mij=1expresses that the the ithpool containsthe jthclone, if not, Mij=0. Considering that there exist errors in the actualexperiment is often inevitable, a disjunct matrix requires certain error correctingproperty.So the key to pooling design is to study constructions of the disjunct matrix.Because that the smaller the row-to-column ratio of the disjunct matrix is,the largerthe error-correcting capacity, then the better the disjunct matrix performances. Sothe two parameters are mainly considered. At present, there are mainly two methodsof constructing disjunct matrix: the containment relation and the intersection ofsudsets in a finite set. Then, on the basis of this, many experts and scholars did alot of research work and constructed many of diferent disjunct matrices, and gainedideal results. In the paper, based on the two methods, we combine the disjunct matrix withsome graphs to construct some new classes of pooling designs, discuss and analysetheir row-to-column ratios and error correcting property, and find our performancesare better.In chapter1, we mainly introduce the research background of pooling designsand research status, and briefly introduce the main sdudy work of this paper;In chapter2, we first analyse the matrix representation of pooling design, thenfocus on the basic properties and several important theorems of disjunct matrix,which run through the whole paper;In chapter3, we mainly expound and study the first constructing method-containment relation. On the basis of that, several families of disjunct matricesare given. In particular, we construct a new pooling design associated with vertex-colored graphs, which has better property;In chapter4, we elaborate the other constructing method-the intersection ofsubsets in a finite set. We combine the disjunct matrix with some graphs to constructsome new classes of pooling designs, discuss and analyse their row-to-column ratioand error correcting property, and find our performances are better.