I'm trying to wrap my head around this problem. I compute a visibility graph in order for a robot to move around, and an obvious application in this graph is to find a shortest path. Now finding the start and end of this path is not difficult, but to the best of my knowledge the shortest-path algorithm does not run in O(n log n) time which I have been told is possible with "appropriate preprocesing". Is there some feature about visibilty graphs that makes this possible, that anyone can outline?
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