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The shortest path tree (SPT) construction is a critical issue to the high performance routing in an interior network using link state protocols, such as open shortest path first (OSPF) and IS-IS. In this paper, we propose a new efficient algorithm for dynamic SPT update to avoid the disadvantages (e.g. redundant computation) caused by static SPT update algorithms. The new algorithm is based on the understanding of the update procedure to reduce redundancy. Only significant elements that contribute to the construction of new SPT from the old one are focused on. The efficiency of our algorithm is improved because it only pay attention to the edges really count for the update process. The running time for the proposed algorithm is maximum reduced, which is shown through experimental results. Furthermore, our algorithm can be easily generalized to solve the SPT updating problem in a graph with negative weight edges and applied to the scenario of multiple edge weight changes.