| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 106 === In classical group testing, one is given a population N which contains some defective items inside. A group test (pool) is a test on a subset of N. A test is negative if the testing pool contains no defective items and the test is positive if the pool contains at least one defective item but we don’t know which one.
Group Testing is a search methodology. The goal is to use less tests to find all defectives. Mainly, to minimize the number of tests in worst case situation. Formally, we let M(d,n) denote the minimum number of tests if |N| = n and d is the number of defectives. The algorithms designed are then applying to minimize M(d,n). Two basic algorithms are adaptive and non-adaptive algorithms.
The tests designed in an adaptive algorithm may depend on the outcome of previous tests but in a non-adaptive algorithm all tests are carried out simultaneously. Therefore, in general, an adaptive algorithm takes less tests in determining all the defectives.
In this thesis, our study focuses on estimating M(d,n) by using the adaptive algorithms. As a consequence, we further improve the well-known generalized splitting algorithm by Frank K. Hwang. For some pairs (d,n) we are able to determine M(d; n) and for general pairs (d,n) we can close the gap between the number of tests we need and the information lower bound ⌈log_2 C(n,d))⌉.
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