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

arXiv: https://arxiv.org/abs/2109.04809 · HTML: https://mlsanity.com/paper/2109.04809/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 50 references that are in the map.
- First posted on arXiv 10 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics](https://mlsanity.com/paper/2108.12627/) (2021)
- [Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Error](https://mlsanity.com/paper/2108.08780/) (2021)
- [Recursive Experts: An Efficient Optimal Mixture of Learning Systems in Dynamic Environments](https://mlsanity.com/paper/2009.09249/) (2020)
- [Optimal and Efficient Algorithms for General Mixable Losses against Switching Oracles](https://mlsanity.com/paper/2108.06411/) (2021)

## Built on by (most cited first, 4 of 4)

- [A Quadratic Time Locally Optimal Algorithm for NP-hard Equal Cardinality Partition Optimization](https://mlsanity.com/paper/2109.07882/) (2021)
- [A Linearithmic Time Locally Optimal Algorithm for the Multiway Number Partition Optimization](https://mlsanity.com/paper/2203.05618/) (2022)
- [Merging Knockout and Round-Robin Tournaments: A Flexible Linear Elimination Tournament Design](https://mlsanity.com/paper/2203.12011/) (2022)
- [A 2-opt Algorithm for Locally Optimal Set Partition Optimization](https://mlsanity.com/paper/2303.08219/) (2023)

## Abstract (arXiv)

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.