Group Testing on Graphs

• Main Authors: Lee,Meng-Hsun, 李孟勳
• Other Authors: Fu,Hung-Lin
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/02405190278298874964

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.