Cs787: Advanced Algorithms 3.1 Sequence Alignment

The Sequence Alignment problem is motivated in part by computational biology. One of the goals of scientists in this field is to determine an evolutionary tree of species by examining how close the DNA is between two potential evolutionary relatives. Doing so involves answering questions of the form “how hard would it be for a species with DNA ‘AATCAGCTT’ to mutate into a species with DNA ‘ATCTGCCAT’?” Formally stated, the Sequence Alignment problem is as follows: Given: two sequences over some alphabet and costs for addition of a new element to a sequence, deletion of an element, or exchanging one element for another. Goal: find the minimum cost to transform one sequence into the other. (There is a disclaimer here. We assume that only one transformation is done at each position. In other words, we assume that ‘A’ doesn’t mutate to ‘C’ before mutating again to ‘T’. This can be assured either by explicit edict or by arranging the costs so that the transformation from ‘A’ to ‘T’ is cheaper than the above chain; this is a triangle inequality for the cost function.) As an example, we will use the following sequences: