Editing Neighbor joining (section)

=== Complexity ===
Neighbor joining on a set of  <math>n</math> taxa requires <math>n-3</math> iterations.  At each step one has to build and search a <math>Q</math> matrix. Initially the <math>Q</math> matrix is size <math>n\times n</math>, then the next step it is <math>(n-1)\times(n-1)</math>, etc. Implementing this in a straightforward way leads to an algorithm with a time complexity of <math>O(n^3)</math>;<ref>{{Cite journal|date=November 1988|title=A note on the neighbor-joining algorithm of Saitou and Nei.|url=https://academic.oup.com/mbe/article/5/6/729/1044339/A-note-on-the-neighborjoining-algorithm-of-Saitou|journal=Molecular Biology and Evolution|language=en|doi=10.1093/oxfordjournals.molbev.a040527|pmid=3221794|issn=1537-1719|last1=Studier|first1=J. A.|last2=Keppler|first2=K. J.|volume=5|issue=6|pages=729–31|doi-access=free}}</ref> implementations exist which use heuristics to do much better than this on average.<ref>{{Cite journal|last1=Mailund|first1=Thomas|last2=Brodal|first2=GerthS|last3=Fagerberg|first3=Rolf|last4=Pedersen|first4=ChristianNS|last5=Phillips|first5=Derek|date=2006|title=Recrafting the neighbor-joining method|url= |journal=BMC Bioinformatics|volume=7|issue=1|pages=29|doi=10.1186/1471-2105-7-29|pmc=3271233|pmid=16423304 |doi-access=free }}</ref>