We design a lightweight beam-searching algorithm for mobile millimeter-wave systems. We construct and maintain a set of path skeletons, i.e., potential paths between a user and the serving base station to substantially expedite the beam-searching process. To exploit the spatial correlations of the channels, we propose an efficient algorithm that measures the similarity of the skeletons and re-executes the beam-searching procedure only when the old one becomes obsolete. We identify and optimize several tradeoffs between: i) the beam-searching overhead and the instantaneous rate of the users, and ii) the number of users and the update overhead of the path skeletons. Simulation results in an outdoor environment with real building map data show that the proposed method can significantly improve the performance of beam-searching in terms of latency, energy consumption and achievable throughout.