# Load Balancing: The Long Road from Theory to Practice

arXiv: https://arxiv.org/abs/2107.13638 · HTML: https://mlsanity.com/paper/2107.13638/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [Algorithms for Discrepancy, Matchings, and Approximations: Fast, Simple, and Practical](https://mlsanity.com/paper/2209.01147/) (2022)

## Abstract (arXiv)

There is a long history of approximation schemes for the problem of scheduling jobs on identical machines to minimize the makespan. Such a scheme grants a (1+ε)-approximation solution for every ε > 0, but the running time grows exponentially in 1/ε. For a long time, these schemes seemed like a purely theoretical concept. Even solving instances for moderate values of ε seemed completely illusional. In an effort to bridge theory and practice, we refine recent ILP techniques to develop the fastest known approximation scheme for this problem. An implementation of this algorithm reaches values of ε lower than 2/11≈ 18.2% within a reasonable timespan. This is the approximation guarantee of MULTIFIT, which, to the best of our knowledge, has the best proven guarantee of any non-scheme algorithm.