We wanted a scenario where, say, 5 well-placed border points could efficiently represent an area with 5,000 internal points and 10,000 road edges. This would reduce those 10,000 edges to just 5*4/2 = 10 shortcuts for routing through that cluster at a high level – an incredible 1:1000 point ratio and a 30x reduction in edges to consider for the high-level path!
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\underbrace{\biggl[\frac{1}{K}, \; \frac{2}{K}\biggr)}_\textrm{bucket 2},