Consensus Strings from Multiple Alignment

Definition 0.2   Given a multiple alignment 37#37 of a set of strings 44#44, the consensus character in column i of 37#37 is the character that minimizes the summed distance to it from all the characters in column i. Let d(i) denote that minimum sum in column i.

Definition 0.3   The consensus string 59#59 derived from the alignment 37#37 is the concatenation of the consensus characters for each column of 37#37.

Definition 0.4   The alignment error of 59#59 equals 60#60 where l is the number of characters in 59#59

Definition 0.5   The optimal consensus multiple alignment is a multiple alignment 37#37 of an input set 44#44 whose consensus string 59#59 minimizes the alignment error. It can be shown that the optimal consensus multiple alignment is equal to the optimal Steiner string, as defined in section 4.2.3.

We can use the center string (S_c) for approximating the optimal multiple alignment with an alignment error smaller than 61#61 times the optimal alignment error.