How to speed up finding a subset of a given set?
if you map every element in set in S into a bit in a binary number. For set with n elements, we have n bit binary number. the $i$-th number takes 1 if the subset has that element. Then we can use a binary number from $00,...,00$ to $11,...,11$  to represent all the subset.

If you map all your subset into binary numbers, then you are searching in the number space.