A Fast Algorithm for the Optimal Alignment of Three Strings

Lloyd Allison

Journal of Theoretical Biology, 164(2), pp.261-269, doi:10.1006/jtbi.1993.1153, September 1993

Abstract  Ukkonen's (pair-wise) string alignment technique is extended to the problem of finding an optimal alignment for three strings. The resulting algorithm has worst-case time-complexity O(nd2) and space-complexity O(d3), where the string lengths are n and d is the three-way edit-distance based on tree-costs. In practice, the algorithm usually runs in O(n+d3) time. The algorithm is particularly fast when the strings are similar, in which case, d<<n.

Three-way alignment is an important special case in string alignment. Each internal node in an unrooted, binary evolutionary-tree has three neighbours. The algorithm presented can be used as an iterative step in a heuristic multiple-alignment program for more than three strings

Also see [source code].

(Later, also see:
D. R. Powell, L. Allison and T. I. Dix, 'Fast, Optimal Alignment of Three Sequences Using Linear Gap Cost', Journal of Theoretical Biology, 207(3), pp.325-336, doi:10.1006/jtbi.2000.2177, December 2000.)