Two Algorithms for a Reachability Problem in One-Dimensional Space
Two algorithms are proposed to solve a reachability problem among time-dependent obstacles in one-dimensional (1-D) space. In the first approach, the motion planning problem is reduced to a path existence problem in a directed graph. The algorithm is very simple, with running time O(n2), where n is the complexity of obstacles in space-time. The second algorithm uses a sweep-line technique and has running time O(n log2 n). Besides, the latter algorithm can be easily modified to compute a collision-free trajectory, if such trajectories exist.
MSU Digital Commons Citation
Wang, Dajin and Sutner, Klaus, "Two Algorithms for a Reachability Problem in One-Dimensional Space" (1998). Department of Computer Science Faculty Scholarship and Creative Works. 602.