. Clarifications and Corrections

2 The ‘star’ algorithm (tutorial #3 slide 13) can be implemented with the following modification: Instead of step (a) in the loop: a.Align S i to S’ 1 to produce S’ i and S’’ 1 aligned Do: a1.Align S i to S 1 to produce S’ i and S’’ 1 aligned a2.add gaps (to S’ i and S’’ 1 ) where gaps of S’ 1 do not appear in S’’ 1. This is slightly more efficient since iteration i takes O(n 2 +i·n) time instead of O(i·n 2 ). It is more evident now that d(1,i)=D( S 1,S i ) for the approximation-ration analysis. Notice that steps (a1,a2) result in an optimal alignment of S i and S’ 1. (Why is this?) Multiple Sequence Alignment Approximation Algorithm

3 Lifted Tree Alignments Algorithm X v - the set of labels on leaves of the subtree rooted in v. d(v,S) - the optimal cost of v ’s subtree when it is labeled by S Initialization: for leaf v labeled S v - Recurrence: for internal node v with daughters u 1,…u l - S1S1 S2S2 S3S3 S4S4 S6S6 S5S5 S2S2 S4S4 S4S4 S5S5 There was a slight error in the phrasing of the DP algorithm for optimal Lifted Alignment (tutorial #4 slide 11). Modifications are highlighted in red below: Note: the original phrasing allows construction of tree alignments which are not lifted.