Table 2.
Complexity of MUSCLE. Here we show the big-O asymptotic complexity of the elements of MUSCLE as a function of L, the typical sequence length, and N, the number of sequences, retaining the highest-order terms in N with L fixed and vice versa.
| Step | O(Space) | O(Time) |
| K-mer distance matrix | N2 + L | N2L |
| UPGMA | N2 | N2 |
| Progressive (one iteration) | LP2 = NL + L2 | LP2 = N2 + L2 |
| Progressive (root alignment) | NLP = N2 + NL | NLP log N = N2 log N + NL log N |
| Progressive (N iterations + root) | N2 + NL + L2 | N3 + NL2 |
| Refinement (one edge) | NLP + LP2 = N2 + L2 | N2LP + LP2 = N3+ L2 |
| Refinement (N edges) | N2 + L2 | N4+ NL2 |
| TOTAL | N2 + L2 | N4 + NL2 |