All,
I would like to find a way to generate the powerset such that all subsets below the current set can be skipped if a condition is met. I think a concrete example might better explain. Assume our set contains 'A' .. 'D';

A, B, C, D
AB, AC, AD, BC, BD, CD
ABC, ABD, ACD, BCD
ABCD
[download]

I omitted the empty set as it has no practical purposes for my problem. The following re-ordering is an example of the optimization I am hoping to use:

ABCD
    ABC
        AB
            A
            B
        AC
            C
        BC
    ABD
        AD
            D
        BD
    ACD
        CD
    BCD
[download]

So if the condition for 'ABCD' was true, I would skip the entire powerset. If 'ABC' was true I would skip to 'ABD'. If 'ABD' was false but 'AD' was true I would skip to 'BD'.

This exact ordering isn't necessary and I am not sure if it helped explain my desire at all. Ultimately the goal is to generate the powerset for a list of sets but avoid duplication where possible. Using another example:

Set1:  A,B,C,D
Set2:  A,B,C,E
set3:  A,B,C,F,G
[download]

They share sets ABC, AB, AC, BC, A, B, and C so why generate them three times? I have used a similar technique in the past with success but I can't seem to wrap my head around how to do it here. Your thoughts and insights are appreciated.

Update: It was suggested in a /msg that I be more specific about the rules and not assume the examples are sufficient.

• If a set has previously been seen, all subsets of that set can be skipped
• The powerset should be generated in a manner that maximizes the potential for optimization. In other words, A,B,C should be generated before A,C
• No more sets should be generated than would otherwise be done using a straight forward iterative approach. In other words, A, B, C should produce only 7 candidates (or less if optimization possible)

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