Why contract low-degree nodes first instead of high-degree ones?
Contracting a node creates shortcut edges between all pairs of its neighbours. A node with 100 neighbours creates ~5,000 shortcuts; a degree-1 node creates none. Contracting low-degree nodes first adds shortcuts gradually, reducing the overhead when high-degree junctions are processed late.
Answered in
Why Google Maps Computes Shortcuts OfflineContraction Hierarchies precomputes shortcut edges offline so routing queries skip neighbourhood streets and touch only 2,000 nodes in under 10 milliseconds.
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