The current crane erection path computation methods are not easily scalable for assisting engineers to find and evaluate detailed erection plans. A reliable and efficient method to help plan erection paths is required, especially for certain critical erection tasks involving heavy lifting objects and narrow working spaces. In this research, we propose four strategies, namely Hoisting, Boundary, Capacity, and Direction (termed HBCD), to accelerate the computation of the configuration space (C-space) for a telescoping-boom mobile crane. The Hoisting strategy reduces the time of computation by neglecting the cable hoisting degree; the Boundary strategy speeds up the collision detection by progressively checking collision boundaries; the Capacity strategy eliminates the range of configurations that exceed the lifting capacity; and the Direction strategy eliminates the configurations with slewing directions. To validate the proposed strategies, we modeled a telescoping-boom mobile crane widely used in construction, LTM 1040-2.1, and created a virtual construction site to implement the four strategies with a collision-free path finding method and a path refinement method. The results show that these strategies can significantly reduce the processing time of C-space construction from hours to less than 10 min. Engineers can therefore utilize these strategies to accelerate the computation of feasible collision-free erection paths for critical lifting and erection tasks.