Find the intersection of elements of powerset one by one

General Usage Performance
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1 
Let S = { trigon, tetragon , pentagon , ... ,... } is a set of polygons

How to calculate intersection of subsets of (every element actually) Powerset(S)

Powerset(S) =[ {} , {trigon} , {tetragon} , {pentagon} , {trigon, tetragon} , {trigon,pentagon} ,......]

for i in Powerset(S)
  find intersect(i)

I need really fast algorithm, is there any solution?
intersection funtion is so expansive and therefore I want minimize this

Are dynamic programming solutions suitable for this?

find every node intersection

intersect( a, b,c ) = intersect( intersect ( a,b), c)

2

Dynamic programming will help a lot here, but the much better method is to not do this in the first place. This operation inherently has exponential time relative to the number of polygons.

3

Can you say something about time complexity?

4

S is a set with 2^n elements in it. You want to allocate an object for each of those. That’s a ton of time if n isn’t very small (less than 15 or so)