Dynamic Programming Solution

The best multiple alignment of r sequences is calculated using an r-dimensional hyper-cube D, defining 4#4 to be the best score for aligning the prefixes of lengths 5#5 of the sequences 6#6, respectively.
We define

7#7

And we calculate

8#8

where 9#9 is the cost function. The size of the hyper-cube is 10#10, where n_j is the length of x_j, where computation of each of each entry consider 2^r -1 others.
If 11#11, the space complexity is of O(n^r) and the time complexity is of O(2^r n^r).