Consistency

Potentials give non-negative reduced weights. Dijkstra applicable.

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Johnson's algorithm

Bellman-Ford from dummy source computes potentials. Then V Dijkstras on reweighted graph. All-pairs shortest paths.

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ALT (A* Landmarks + Triangle)

Precompute distances to landmarks. Landmark triangle inequality → potentials. Point-to-point queries fast.

Complexity

Depends on preprocessing choice. Point-to-point: ms on continent-scale.