Performance Limitation of Group Testing in Network Failure Detection

In a network system, there inevitably be few connection failures at nodes, such as delay. Once failure occurs, the administrator must detect sources soon possible to maintain communication over network. Group testing is method for detecting nodes in networks using small number of measurements, provided that measurement matrix constructed appropriately. A promising constructing matrices given by binary correlation matrices. This study analyzes performance limitation group based on matrix. We derive upper and lower bounds minimum measurements needed detection. Moreover, we propose sufficient condition topology, under which vertices can detected with optimal performance, also provide detection scheme guaranteed exactness Numerical example indicates satisfies proposed condition, exactly our scheme.