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I am trying to find as many pairs of elements as possible from two distinct data streams, while being constrained by the number of elements I can hold in memory at any given time. Once a pair of elements is found, it can be removed from memory.

This problem feels like a streaming variant of the maximum coverage problem, except that I'm trying to figure out the optimal strategy for determining which elements I should keep and which ones I should prune when a new element arrives and my data structure is at its maximum capacity.

More generally, I would like to find which classical problem this can be reduced to.

A more formal phrasing of my question would be : given two streaming multisets of integers $S_1$ and $S_2$ and a positive integer capacity $C$, what is the optimal strategy to find the maximum number of pairs of identical integers from $S_1$ and $S_2$ such that at any point, the number of integers in memory is less than $C$ ?

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