The algorithm walks the tree recursively. At each node, it checks: does this node's bounding box overlap with the query rectangle? If not, the entire subtree gets pruned (skipped). If it does overlap, it tests the node's points against the query and recurses into the children.
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.
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