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Trajectory reconstruction of mobile targets in large-scale infrastructure enables events in a range of applications, such as regional security, tourism, and healthcare, to be visualized. However, indoor environmental factors complicate the reconstruction process, usually resulting in reduced efficiency. In this article, we propose a searching algorithm that aims at a reasonable trajectory reconstruction scheme. The algorithm is developed based on the branch-and-bound method, which incorporates both depth-first search and breadth-first search so that a fast trajectory reconstruction on a topological map becomes viable. Experimental results demonstrated that the considered strategies are effective in accelerating reconstruction through a performance evaluation against current approaches for trajectory reconstruction.