Causal Domain Restriction Techniques.
Zachary Clawson (Center for Applied Mathematics, Cornell)

Dijkstra's method is one of the most efficient algorithms for computing shortest paths on a graph (from multiple sources to a single target). However, Dijkstra's method is far less efficient for solving single-source/single-target problems, where much of the graph becomes irrelevant (away from the optimal path). Methods such as the A* algorithm modify Dijkstra's to steer computations closer to the optimal path using consistent heuristic bounds.

The same ideas may be adapted to compute continuous single-source/single-target optimal trajectories efficiently. Unlike in the graph case, here this results in additional errors depending on grid size and the aggressiveness of restriction. We explore computational efficiency and accuracy of both pre-existing and newly introduced techniques. We expect these methods to be particularly useful for higher-dimensional problems, in which refining the mesh in the entire domain is prohibitively costly.