Table 4. Unweighted Landmark Isomap Computational Complexity.

Unweighted Landmark Isomap Computational Complexity
Step	Worst-case complexity	Further Explanation
Step 2	𝓞(ℓ⋅n)	[13]
Step 3	𝓞(ℓ⋅m)	A breadth first search has a complexity of 𝓞(m). This is done for each of ℓ landmark points. If the graph had been weighted (as assumed in standard Landmark Isomap), then we would need to use Dijkstra’s algorithm. The fastest general implementation is 𝓞(m + n⋅log n) [30] for each landmark point, yielding 𝓞(ℓ⋅m + ℓ⋅n⋅log n).
Step 4	𝓞(ℓ 3)	[13]
Step 5	𝓞(k⋅ℓ⋅n)	[13]
Total	𝓞(ℓ⋅m + k⋅ℓ⋅n + ℓ 3)