High-level description of our algorithm to calculate a multiple alignment of a set of input sequences s1, . . ., s
. The algorithm calculates a first alignment A0 using our novel progressive approach and a second alignment A1 with the greedy method previously used in DIALIGN. Finally, the alignment with the higher numerical score is returned. For the progressive method, fragments, i.e. local gap-free pairwise alignments from the respective optimal pairwise alignments are considered. Fragments with a weight score above the average fragment score are processed first following a guide tree as described in the main text. Lower-scoring fragments are added later, provided they are consistent with the previously included high-scoring fragments. Note that the output of the sub-routine PAIRWISE_ALIGNMENT is a chain of fragments. This is equivalent to a pairwise alignment in the sense of DIALIGN.