Needleman and Wunsch [13] suggested that their dynamic
programming algorithm could be extended to the comparison of many
sequences. Waterman *et al. * [27] also described how dynamic
programming could be used to align more than two sequences. In
practice, the need to store an dimensional array (where is the
number of sequences) limits these extensions to three-sequence
applications. In addition, the time required to perform the
comparison of three sequences is proportional to . Murata *et al. *
[44] described a modification of the Needleman and Wunsch
procedure for three sequences which ran in time proportional to
; unfortunately this approach required an additional three
dimensional array thus further limiting its application to short
sequences. One of the earliest practical applications of dynamic
programming to multiple alignment was the work of Sankoff *et al. *
[45] who aligned nine 5S RNA sequences that were linked by
an evolutionary tree. Their algorithm which also constructed the
protosequences at the interior nodes of the tree was made
computationally feasible by decomposing the nine-sequence problem into
seven three sequence alignments. The alignments were repeatedly
performed working in from the periphery of the tree until no further
change occurred to the protosequences.

geoff.barton@ox.ac.uk