A quadtree does the same thing for two-dimensional space. It takes a rectangular region and divides it into four equal quadrants: northwest, northeast, southwest, southeast. If a quadrant has too many points in it, it subdivides again and again. Each subdivision creates smaller and smaller cells where points are densely packed.
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This step rapidly finds the optimal sequence of border points and shortcuts to get from your start cluster's periphery to your target cluster's periphery. It's incredibly fast because it's ignoring all the tiny roads within intermediate clusters.