Multiple Alignment with Consensus

In this section we look at an approximation algorithm for a multiple alignment that optimizes a different score metrics - the consensus error. As before, we assume the existence of a pairwise scoring scheme 53#53 satisfying the triangle inequality.

Definition 0.1   Given a set of strings 44#44, the consensus error of a string 54#54 with respect to 44#44 is 55#55. Note that 54#54 need not be in 44#44.

56#56
The Steiner string S^* attempts to capture the common characteristics of the set of strings 44#44 and reflect them in a single string. We will present an approximation algorithm for the optimal Steiner string problem with worst-case approximation ratio of 2.
 57#57

58#58
It is worthwhile noting that Steiner string was defined without alignment, and the only requirement is the distance function, that satisfies the triangle inequality. We will next start discussing consensus strings that are alignment motivated.