Shortcut Pre-calculation: For the most commonly used speed profiles, the travel costs (time/distance) for shortcuts between border points within each cluster are pre-calculated and stored. (Each border point effectively has an "entry" and "exit" aspect for directed travel).
Notice how the highlighted region shrinks at each step. The algorithm never examines points outside the narrowing window. In a balanced tree with nnn points, this takes about log4(n)\log_4(n)log4(n) steps. For a million points, that's roughly 10 steps instead of a million comparisons.
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