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We proposed in a previous paper (2006) a hybrid two-layered approach for motion planning of multiple agents in static virtual environments, consisting of open spaces connected by multiple narrow passages. The discrete generalized Voronoi diagram (GVD) of the environment is used to identify narrow passages, and plan the global path of each agent independently of other agents' global paths. As each agent moves along its global path, the agent's path is locally modified using the hybrid technique of combining steering behaviors with Coordination Graphs (CG), where coordination graphs are used for deadlock avoidance in the narrow passages. The planner in the previous paper was single threaded, and it was able to plan the motions of 30 agents moving around in a simple virtual environment with 3 narrow passages. If more agents are moving in a more complex virtual environment (i.e., with more narrow passages), we may not be able to construct and process all the coordination graphs in real-time. In this paper, we parallelize the single threaded planner in a supervisor-worker paradigm with Unix processes who communicate with each other using System V interprocess communication (IPC) mechanism. We show that significant, scalable speedups are obtained by constructing and processing coordination graphs in parallel on a symmetric multiprocessing (SMP) system.