Graph-Constrained Group Testing

Non-adaptive group testing involves grouping arbitrary subsets of n items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most d defective items. Motivated by applications in network tomography, sensor networks and infection propagation, a variation of group testing problems on graphs is formulated. Unlike conventional group testing problems, each group here must conform to the constraints imposed by a graph. For instance, items can be associated with vertices and each pool is any set of nodes that must be path connected. In this paper, a test is associated with a random walk. In this context, conventional group testing corresponds to the special case of a complete graph on n vertices. For interesting classes of graphs a rather surprising result is obtained, namely, that the number of tests required to identify d defective items is substantially similar to what req...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Mahdi Cheraghchi, Amin Karbasi, Soheil Mohajer, Venkatesh Saligrama
• Keywords: Conventional Group, CORR 2010, Defective Items, Education, Group