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Waypoint graph is often used for pathfinding due to its advantage in specifying the space and obstacles in a region. Currently the waypoint graph based pathfinding suffers from large computation overhead and hence long latency in dynamic environment, where the location of obstacles may change. In this paper, we propose a fast approach for waypoint graph based pathfinding in such scenario. We eliminate unnecessary waypoints and edges to make the graph sparse. And then we design a prediction-based local method to handle the dynamic change in the environment. 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