Minimum Number of Measurements in Enhanced Group Testing for Failure-edge Detection in Networks

In a network system, there might be a few connection failures over the links. To maintain the stability of the system, the administrator has to detect failure sources as soon as possible. This paper aims at solving the problem of detecting failure edges on graphs via a few measurements. By using the enhanced group testing with analog measurements and combining the knowledge of sparse reconstruction, we derive the tight lower bound of needed measurements for the diagnosis. Our result reduces the number of measurements than the previous research, which is expected to improve the detection efficiency and reduce the cost of diagnosis.