7

Announcements: read ch. 7

Computing the final score in O(n) space

Values on the previous column are all that are needed for the next

Final score is the max of the last column

What about reconstructing an optimal alignment?

Constructing the alignment

Any optimal path must go through one edge through the midpoint

The big idea:

Generalization: graph cuts

At the heart of this trick

• The DAG can be cut into equal pieces with 2n edges
• The computation on one piece can be reversed

Iterating

Total time: O(nm), Total space: O(n)

A "Block Alignment" grid

We divide the grid into blocks and only compute scores at the corners

Places where we compute scores

Solve the blocks, then knit the blocks together

If we solved the mini-alignments by DP we'd be back to O(nm).

Is there any advantage to solving the mini-alignments by DP?

Make a table of all possible mini-alignment blocks

If the block sizes are small enough, this is not too crazy an idea. This is really nothing more than creating a product alphabet. Another example of computation sharing

Allowing unrestricted entrance and exit

A more complicated lookup

What about more general alignment

Alignment mini-review

Global alignment

• Local alignment
• Affine (or convex) gap penalty
• Multi-alignment (or progressive)
• Amino acid to nucleotide alignment
• Space efficient (or cache efficient)
• Sub-quadratic runtime

All these factors are nearly orthogonal (the last two might not be)

We've discussed each one in isolation

Great effort to code simultaneously (an opportunity for someone)