Efficient Locally Optimal Number Set Partitioning for Scheduling, Allocation and Fair Selection

We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and requires exponential complexity to solve (i.e., intractable); we formulate a weaker version of this NP-hard problem, where the goal is to find a locally optimal solution. We show that our proposed algorithms can find a locally optimal solution in near linear time. Our algorithms require neither positive nor integer elements in the input set, hence, they are more widely applicable.