# Speed-Robust Scheduling -- Sand, Bricks, and Rocks

arXiv: https://arxiv.org/abs/2011.05181 · HTML: https://mlsanity.com/paper/2011.05181/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Overcoming Brittleness in Pareto-Optimal Learning-Augmented Algorithms](https://mlsanity.com/paper/2408.04122/) (2024)
- [Scheduling with Speed Predictions](https://mlsanity.com/paper/2205.01247/) (2022)
- [Speed-Oblivious Online Scheduling: Knowing (Precise) Speeds is not Necessary](https://mlsanity.com/paper/2302.00985/) (2023)

## Abstract (arXiv)

The speed-robust scheduling problem is a two-stage problem where given m machines, jobs must be grouped into at most m bags while the processing speeds of the given m machines are unknown. After the speeds are revealed, the grouped jobs must be assigned to the machines without being separated. To evaluate the performance of algorithms, we determine upper bounds on the worst-case ratio of the algorithm's makespan and the optimal makespan given full information. We refer to this ratio as the robustness factor. We give an algorithm with a robustness factor 2-1/m for the most general setting and improve this to 1.8 for equal-size jobs. For the special case of infinitesimal jobs, we give an algorithm with an optimal robustness factor equal to e/(e-1) ≈ 1.58. The particular machine environment in which all machines have either speed 0 or 1 was studied before by Stein and Zhong (SODA 2019). For this setting, we provide an algorithm for scheduling infinitesimal jobs with an optimal robustness factor of (1+√2)/2 ≈ 1.207. It lays the foundation for an algorithm matching the lower bound of 4/3 for equal-size jobs.