Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure the effective resistance between certain pairs of nodes (which can be done by measuring the amount of current when one unit of voltage difference is applied at the chosen pair of nodes). The goal is to determine which edge, if any, is not working in the network using the smallest number of measurements. We prove rigorous upper and lower bounds on this optimal number of measurements for different classes of graphs. These bounds are tight for several of these classes showing that our measurement strategies are optimal.

翻译：给定一个电阻网络，我们希望确定网络中所有电阻（边）是否正常工作，若非如此，则需识别出具体哪条（或哪些）边存在故障。为进行此判定，我们允许测量特定节点对之间的等效电阻（这可通过在选定节点对上施加单位电压差并测量电流值来实现）。目标是以最少的测量次数确定网络中是否存在故障边及其具体位置。我们针对不同图类证明了该最优测量次数的严格上下界。对于其中多类图，这些界是紧致的，表明我们所提出的测量策略具有最优性。