algorithm for 'best subsets'

[halley]

I have a data structure which is similar to the following. The actual structure is not important, just that we're dealing with a number of "sets" of keywords, some of which are shared between items, and many of which are not.

%items = ( z => [ qw/one six/ ],
           y => [ qw/two three five/ ],
           x => [ qw/one two five/ ],
           ...
         );

Each item's keywords are unique. The arrays could just as easily be keys of hashes, but in this case, they just happen to be stored in arrays.

I can pretty easily scan the set of items for those with the most keywords, or scan for the set of keywords which appear in the most items.

What I would like to do is to figure out which pairs of keywords or triples of keywords or n-ples of keywords are shared by the most items. For example, if keyword A is found in ten items, and keyword B is found in twenty items, but only 1 item has both A and B, then it's a weak candidate. If nine items have both A and B, then it's a great candidate.

In Google terms, think of it this way: from the database of websites, what would be the best four-word query to include the most results links? And then the second-best four-word query? And the third-best four-word query? And so on...

Ideas? Does this align with some obscure or obvious algorithm I couldn't recognize?

Update: A test-case-generator function has been added below. Use this data if you'd like to do some benchmarking on your own.

Update 2: A sample output from an early timeline scanner has been added below.