Naive
Johnson's APSP + max. O(V² log V + VE) with Dijkstra × V.
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Random BFS estimation
BFS from random vertex → eccentricity ≥ ecc(random)/2. Bound within factor 2 quickly.
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Chan's algorithm
Exact diameter in Õ(V²) for undirected unweighted via matrix multiplication tricks.
Roditty-Vassilevska
Under Strong Exponential Time Hypothesis, no O(V^(2-ε)) exact diameter algorithm exists.