The subset sum problem is not in P because the question is about lossy compressed data? Why not?
The subset sum problem is quite different from your problem: Given a list of integers and a target sum $S$, it asks if there is a subset of the list that sums to $S$. No &quot;compression&quot;, lossy or not. Any lossy technique will (by definition) tend to miss the target (because it works with an approximation). And we are looking for an exact solution, not one that is 10% off, it has to be right on.
It looks to me that the collection of subsets for which you need to compute the sums is even larger than the numbers in the original list. If so, it isn't any speedup.