Algorithm: Removing as few elements as possible from a set in order to enforce no subsets.

Posted by phimuemue on Stack Overflow See other posts from Stack Overflow or by phimuemue
Published on 2010-05-19T11:59:05Z Indexed on 2010/05/19 12:20 UTC
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Hello, I got a problem which I do not know how to solve:

I have a set of sets A = {A_1, A_2, ..., A_n} and I have a set B.

The target now is to remove as few elements as possible from B (creating B'), such that, after removing the elements for all 1 <= i <= n, A_i is not a subset of B'.

For example, if we have A_1 = {1,2}, A_2 = {1,3,4}, A_3={2,5}, and B={1,2,3,4,5}, we could e.g. remove 1 and 2 from B (that would yield B'={3,4,5}, which is not a superset of one of the A_i).

Does anybody know an algorithm for determining the (minimal number of) elements to be removed?

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