Fast Approximation to the NP-hard Problem of Multiple Sequence Alignment

The study and comparison of several sequences of characters from a nite alphabet is relevant to various areas of science, in particular molecular biology. It has been shown that multiple sequence alignment with the sum-of-pairs score is NP-hard. Recently a fast heurstic method was proposed based on a Divide-and-Conquer technique. Recursively, all sequences were cut at some suitable positions. Eventually, the sets of subsequences were aligned optimally. In general, the (time) complexity of searching for good cutting points is O(l n) (n the number and l the maximal length of the sequences involved). By a simple (n l)-time technique, the base l was reduced, leading to a reasonable fast alignment algorithm for up to n = 7 and l 500. We reene the base-reducing technique by spending computational time quad-ratic in n (and still linear in l). This improves the alignment procedure regarding the number of sequences managable up to n = 9 (of same length l). Moreover, we present two natural extensions of this technique. One is an iterative application of a (n 2 l)-time technique and therefore still of that complexity. The other needs time O(n 2 l s+1), where s is the number of sequences simultaneously considered during a minimization procedure.