Efficient Algorithms for Partitioning Problems with Bounded Splittings and Interval Targets

The authors study three variants of the classic n-way number partitioning problem that relax the constraints of the original problem. The first two variants allow a bounded number of split items or splittings, while the third variant requires the largest bin sum to be within a pre-specified interval. The authors provide a complete picture of the computational complexity of these variants, showing that they can be solved efficiently in polynomial time in certain parameter regimes, while remaining NP-complete in others.