Consider a robot traversing a graph-modeled space and attempting to ascertain its present location. To determine its distance from each fixed landmark, a signal can be sent between them. Both figuring out the ideal amount of markers and where to put them are covered. Because this problem is NP-complete, the robot responds to the actions slowly. To expedite this response, a parallel version of this challenge will be employed. A new parallel technique for determining the graph’s metric dimension is presented in this study. The suggested approach is implemented on a cluster with symmetric multiprocessing (SMP). Lastly, four major graph groups—the tracks the robot is traveling on—are used to verify the implementation. When tested on eight processors, the simulation results demonstrate the potential of the suggested parallel approach, which achieved a six-fold speedup.