| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 104 === The idea of group testing originated from the blood testing in 1943 by Dorfman. Li was
the first who studied the combinatorial group testing as follows. Consider a population
V of n items consisting of an unknown subset D Ď V of d defectives. The problem is to
identify the set D by a sequence of group tests. Each test is on a subset X of V with two
possible outcomes: a negative outcome indicates that X X D = H, a positive outcome
indicates that X X D H. The goal is to minimize the number M[d; n] of tests under
the worst scenario.
This thesis mainly studies group testing on bipartite graphs. That is, the set of items
are separated into two disjoint subsets and a defective complex comes from these two
sets one from each. By associating each item with a vertex, the sample space can be
represented by a bipartite graph where each edge represents a sample point of the space
S(2; n). In order to show this problem, Chang and Hwang conjectured that a bipartite
graph with 2k(k ą 0) edges always has a subgraph, induced by a subset of vertices, with
exactly 2k1 edges. If this conjecture is true then a binary splitting algorithm can be
applied to determine the defective complexes with minimum number of tests in sequential
algorithm. While the conjecture remains open, it has stimulated my forthcoming reserach
casting group testing on graphs.
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