Towards the 5/6-Density Conjecture of Pinwheel Scheduling
Abstract
Pinwheel Scheduling aims to find a perpetual schedule for unit-length tasks on a single machine subject to given maximal time spans (a.k.a. frequencies) between any two consecutive executions of the same task. The density of a Pinwheel Scheduling instance is the sum of the inverses of these task frequencies; the 5/6-Conjecture (Chan and Chin, 1993) states that any Pinwheel Scheduling instance with density at most 5/6 is schedulable. We formalize the notion of Pareto surfaces for Pinwheel Scheduling and exploit novel structural insights to engineer an efficient algorithm for computing them. This allows us to (1) confirm the 5/6-Conjecture for all Pinwheel Scheduling instances with at most 12 tasks and (2) to prove that a given list of only 23 schedules solves all schedulable Pinwheel Scheduling instances with at most 5 tasks.
Keywords
Cite
@article{arxiv.2111.01784,
title = {Towards the 5/6-Density Conjecture of Pinwheel Scheduling},
author = {Leszek Gąsieniec and Benjamin Smith and Sebastian Wild},
journal= {arXiv preprint arXiv:2111.01784},
year = {2021}
}
Comments
Accepted at ALENEX 2022