An example application is identical-machines scheduling where each machine has a job-queue that can hold at most k jobs.
[3] A common special case called two-way balanced partitioning is when there should be two subsets (m = 2).
It is NP-hard to decide whether there exists a partition in which the sums in the two subsets are equal; see [4] problem [SP12].
There are many algorithms that aim to find a balanced partition in which the sum is as nearly-equal as possible.
Another special case called 3-partitioning is when the number of items in each subset should be at most 3 (k = 3).
Deciding whether there exists such a partition with equal sums is exactly the 3-partition problem, which is known to be strongly NP-hard.
There are approximation algorithms that aim to find a partition in which the sum is as nearly-equal as possible.
A more general case, called k-partitioning,[12] is when the number of items in each subset should be at most k, where k can be any positive integer..
He, Tan, Zhu and Yao[16] present an algorithm called HARMONIC2 for maximizing the smallest sum with different cardinality constraints.
That is, kh = 1 for each category h. Matroid-constrained number partitioning is a generalization in which a fixed matroid is given as a parameter, and each of the m subsets should be an independent set or a base of this matroid.