I have groups of students that need to be allocated into classrooms of a fixed capacity (say, 100 chairs in each).
Each group must only be allocated to a single classroom, even if it is larger than the capacity (ie there can be an overflow, with students standing up)
I need an algorithm to make the allocations with minimum overflows and under-capacity classrooms.
A naive algorithm to do this allocation is horrendously slow when having ~200 groups, with a distribution of about half of them being under 20% of the classroom size.
Any ideas where I can find at least some good starting point for making this algorithm lightning fast?
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