Largest number of unique values in sets Let's say I have 100 sets of values, and each set contains roughly 100,000 values.  From these sets, I want to find the 10 sets that collectively have the largest number of unique values.

The brute force method of just checking all combinations is a combinatorial nightmare.  I also thought about doing a rough approach (solution doesn't have to be perfectly optimal) of just finding 'the next best set' to add in sequence.  So finding the largest set, then checking each of the rest of the 99 sets for smallest overlap, then checking the next 98 sets for smallest overlap, etc, but that's still 100+99+98+97+96+95+94+93+92+91 = 955 things to do.

Is there something more efficient?
Your problem is known as Maximum coverage. The greedy algorithm (repeatedly take a set which covers the maximum number of uncovered elements) is a $1-1/e$ approximation, and runs quite efficiently.