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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.

From: MUSCLE: a multiple sequence alignment method with reduced time and space complexity

Step O(Space) O(Time)
K-mer distance matrix N2 + L N 2 L
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 N 4 + NL 2
TOTAL N2 + L2 N4 + NL2