Alignment Graph

It is often useful to represent dynamic programming solutions of sequence problems in terms of a weighted graph.  
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1.

((i,j),(i+1 , j)) with weight 31#31

2.

((i , j+1)) with weight 32#32

3.

((i,j),(i+1 , j+1)) with weight 33#33

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.

 

Figure 2.4: Alignment Graph. The alignment graph is a direct acyclic graph. On the right side of the figure one can see the segment of the alignment graph. It represents the three possibilities at each stage of the algorithm.

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