| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 103 === Abstract
Group testing involves identifying at most d defective items out of a set N of n items. In classical group testing problems, queries on all possible non-empty subsets S of N are used. Formally for the pool S, we use Q(S) = 1 to denote that there exists at least one defective in S ( but we don’t know which ones ) and Q(S) = 0 otherwise. If we are able to determine the number of t positives in a test, then Q(S) = t is used to denote the outcome. For convenience, this type of group testing is referred to as a group testing with quantitative outcome. This is the kind of testing we study in this thesis.
Based on pratical applications in many fields, the size of S has its limitation comparing to the number of items. For example, in blood testing problem proposed by Dorfman (1943), we test around 10 items each time for hundreds and thousands to be tested. This also motivates us to study the effect when the pool size in bounded.
The main focus of the study is to determine the number of tests ( adaptive algorithm ) we need in identifying d positives out of a set of n items. So, we first provide an upper bound of this number in worst case for various n and d, and then we also study the average number of tests we need in an adaptive algorithm.
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