Table 2 

Complexity of MUSCLE. Here we show the bigO asymptotic complexity of the elements of MUSCLE as a function of L, the typical sequence length, and N, the number of sequences, retaining the highestorder terms in N with L fixed and vice versa. 

Step 
O(Space) 
O(Time) 


Kmer distance matrix 
N^{2 }+ L 
N^{2}L 
UPGMA 
N^{2} 
N^{2} 
Progressive (one iteration) 
L_{P}^{2 }= NL + L^{2} 
L_{P}^{2 }= N^{2 }+ L^{2} 
Progressive (root alignment) 
NL_{P }= N^{2 }+ NL 
NL_{P }log N = N^{2 }log N + NL log N 
Progressive (N iterations + root) 
N^{2 }+ NL + L^{2} 
N^{3 }+ NL^{2} 
Refinement (one edge) 
NL_{P }+ L_{P}^{2 }= N^{2 }+ L^{2} 
N^{2}L_{P }+ L_{P}^{2 }= N^{3}+ L^{2} 
Refinement (N edges) 
N^{2 }+ L^{2} 
N^{4}+ NL^{2} 
TOTAL 
N^{2 }+ L^{2} 
N^{4 }+ NL^{2} 


Edgar BMC Bioinformatics 2004 5:113 doi:10.1186/147121055113 