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Longest Common Subsequence in Postgres - Algorithm Challenge

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I have two relations, where each relation has two fields, one
indicating a name and one indicating a position.  That is, each
relation defines a sequence.

I need to determine their longest common subsequence.  Yes, I can do
this by fetching all the data into Java (or any other language) and
computing it using the standard LCS dynamic programming language.  But
I'd like to stay within Postgres.  Is there any way to do this?


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