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To find these crucial border points, we employed a clever technique based on the Ford-Fulkerson algorithm. By simulating "flooding" roads with traffic from random start/end points, we could identify the natural bottlenecks – the "minimum cut" in graph theory terms. These bottlenecks became our border points.
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For example, a 500km route might be broken down into ~100 such shortcuts. If each A* shortcut calculation explores 100-1000 detailed road segments, the total detailed segments visited by A* might be around 10,000-50,000. Compare this to the 1,000,000+ segments the old A* might have needed for the entire route!
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