Key insight
Hierarchical structure of components at increasing weight scales. Union-Find + component merging.
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Requires
Undirected graph. Integer weights. RAM model (bit tricks + word operations).
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Not directed
No linear-time SSSP known for directed integer graphs. Best remains O(m + n log log n) via Han-Thorup.
Practical impact
Constants HUGE. Not implemented in practice. Theoretical breakthrough.