## Fast, Optimal Alignment of Three Sequences Using Linear Gap Cost

#### D. R. Powell, L. Allison & T. I. Dix,
Journal of Theoretical Biology, 207(3), pp.325-336,
doi:10.1006/jtbi.2000.2177,
Dec. **2000**

**Abstract**:
Alignment algorithms can be used to infer a
relationship between sequences when the true relationship is unknown.
Simple alignment algorithms use a cost function that gives a fixed cost to
each possible point mutation-mismatch, deletion, insertion.
These algorithms tend to find optimal alignments that have many small gaps.
It is more biologically plausible to have fewer longer gaps rather than
many small gaps in an alignment. To address this issue,
linear gap cost algorithms are in common use for aligning biological sequence
data. More reliable inferences are obtained by aligning more than
two sequences at a time. The obvious dynamic programming algorithm for
optimally aligning k sequences of length n runs in O(nk) time.
This is impractical if k>3 and n is of any reasonable length.
Thus, for this problem there are many heuristics for aligning k sequences,
however, they are not guaranteed to find an optimal alignment.
In this paper, we present a new algorithm guaranteed to find the
optimal alignment for three sequences using linear gap costs.
This gives the same results as the dynamic programming algorithm for
three sequences, but typically does so much more quickly.
It is particularly fast when the (three-way) edit distance is small.
Our algorithm uses a speed-up technique based on Ukkonen's
greedy algorithm (Ukkonen, 1983) which he presented for two sequences and
simple costs.

Full paper here: [doi:10.1006/jtbi.2000.2177][4/'03].