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Trajectory simplification has become a research hotspot since it plays a significant role in the data preprocessing, storage, and visualization of many offline and online applications, such as online maps, mobile health applications, and location-based services. Traditional heuristic-based algorithms utilize greedy strategy to reduce time cost, leading to high approximation error. An Optimal Trajectory Simplification Algorithm based on Graph Model (OPTTS) is proposed to obtain the optimal solution in this paper. Both min-# and min-ε problems are solved by the construction and regeneration of the breadth-first spanning tree and the shortest path search based on the directed acyclic graph (DAG). Although the proposed OPTTS algorithm can get optimal simplification results, it is difficult to apply in real-time services due to its high time cost. Thus, a new Online Trajectory Simplification Algorithm based on Directed Acyclic Graph (OLTS) is proposed to deal with trajectory stream. The algorithm dynamically constructs the breadth-first spanning tree, followed by real-time minimizing approximation error and real-time output. Experimental results show that OPTTS reduces the global approximation error by 82% compared to classical heuristic methods, while OLTS reduces the error by 77% and is 32% faster than the traditional online algorithm. Both OPTTS and OLTS have leading superiority and stable performance on different datasets

A Graph-Based Min-# and Error-Optimal Trajectory Simplification Algorithm and Its Extension towards Online Services