To which field does this belong?

Which field of mathematics would describe an algorithm to solve the
problem below? What keywords should I use to point me in the right
direction?

Problem:
I have a set of n distinct elements T = {e_1, e_2, ..., e_n}, and m
subsets of T, S_1, S2, ... S_m, that can overlap.
I need to find the minimum number of subsets whose union equals T.


Thanks,
Hari

.

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