Multi Agent Path Finding (MAPF) is critical for coordinating multiple robots in shared environments, yet robust execution of generated plans remains challenging due to operational uncertainties. The Action Dependency Graph (ADG) framework offers a way to ensure correct action execution by establishing precedence-based dependencies between wait and move actions retrieved from a MAPF planning result. The original construction algorithm is not only inefficient, with a quadratic worst-case time complexity it also results in a network with many redundant dependencies between actions. This paper introduces two key improvements to the ADG framework. First, we prove that wait actions are generally redundant and show that removing them can lead to faster overall plan execution on real robot systems. Second, we propose an optimized ADG construction algorithm, termed Sparse Candidate Partitioning (SCP), which skips unnecessary dependencies and lowers the time complexity to quasi-linear, thereby significantly improving construction speed.
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