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Detecting errors in traffic trajectories (i.e., packet forwarding paths) is important to operational networks. Several different traffic monitoring algorithms such as Trajectory Sampling, PSAMP, and Fatih can be used for traffic trajectory error detection. However, a straight-forward application of these algorithms will incur the overhead of simultaneously monitoring all network interfaces in a network for the packets of interest. In this paper, we propose a novel technique called router group monitoring to improve the efficiency of trajectory error detection by only monitoring the periphery interfaces of a set of selected router groups. We analyze a large number of real network topologies and show that effective router groups with high trajectory error detection rates exist in all cases. However, for router group monitoring to be practical, those effective router groups must be identified efficiently. To this end, we develop an analytical model for quickly and accurately estimating the detection rates of different router groups. Based on this model, we propose an algorithm to select a set of router groups that can achieve complete error detection and low monitoring overhead. Finally, we show that the router group monitoring technique can significantly improve the efficiency of trajectory error detection based on Trajectory Sampling or Fatih.