The.Algorithm.Design.Manual.Springer-Verlag.1998

War Story: Evolution of the Lobster
Figure: Morphing a lobster into a head via dynamic programming
● Full run match: We may match run i on top to run j on the bottom for a cost that is a function of
the difference in the lengths of the two runs and their positions.
● Merging runs: We may match a string of consecutive runs on top to a run on the bottom. The cost
will be a function of the number of runs, their relative positions, and their lengths.
● Splitting runs: We may match a big run on top to a string of consecutive runs on the bottom. This
is just the converse of the merge. Again, the cost will be a function of the number of runs, their
relative positions, and their lengths.
``For each pair of runs (i,j) and all the cases that apply, we compute the cost of the edit operation and add
to the (already computed and stored) edit cost to the left of the start of the edit. The cheapest of these
cases is what we will take for the cost of c[i,j].''
The pair of graduate students scribbled this down, then frowned. ``So we are going to have a cost
measure for matching two runs that is a function of their lengths and positions. How do we decide what
the relative costs should be?''
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