### Re^4: longest common substring

by lima1 (Curate)
 on Jan 03, 2008 at 07:24 UTC ( #660131=note: print w/replies, xml ) Need Help??

in reply to Re^3: longest common substring

I think the best exact solutions for the longest common subsequence problem are the dynamic programming ones. But this is only reasonable for 2-4 strings (0(n^2) to O(n^4)). So people use heuristics. A trivial one is to calculate a simple (tree) clustering with something like UPGMA. For example:
```\$a='AAAB';
\$b='AABB';
\$c='ABBB';
\$d='BBBB';

+---\$a
+----+
|    +---\$b
|
+
|
|    +---\$c
+----+
+---\$d
Then you calculate the subsequences of the leafs (a,b) and (c,d) and in the next step (according some special rules) the subsequences of the subsequences.

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