Alignment Graph

It is often useful to represent dynamic programming solutions of string problems in terms of a weighted graph.

 

1.

((i,j),(i+1 , j)) with weight $\sigma(S_{i+1}, -)$

2.

((i , j+1)) with weight $\sigma( - , T_{j+1})$

3.

((i,j),(i+1 , j+1)) with weight $\sigma(S_{i+1}, T_{j+1})$

A path from node (0, 0) to node (n, m) in the alignment graph corresponds to an alignment and its total weight is the alignment score. Our goal is to find the heaviest path from node (0,0) to node (n,m).

This alignment graph is used to map the problem of optimal alignment into the world of graphs, opening the door for new and exciting algorithms.