Path planning is crucial for the efficient operation of Autonomous Mobile Robots (AMRs) in factory environments. Many existing algorithms rely on Dubins paths, which have been adapted for various applications. However, an efficient method for directly determining the shortest Dubins path remains underdeveloped. This paper presents a comprehensive approach to efficiently identify the shortest path within the Dubins set. We classify the initial and final configurations into six equivalency groups based on the quadrants formed by their orientation angle pairs. Paths within each group exhibit shared topological properties, enabling a reduction in the number of candidate cases to analyze. This pre-classification step simplifies the problem and eliminates the need to explicitly compute and compare the lengths of all possible paths. As a result, the proposed method significantly lowers computational complexity. Extensive experiments confirm that our approach consistently outperforms existing methods in terms of computational efficiency.