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arXiv · 2111.01784

Towards the 5/6-Density Conjecture of Pinwheel Scheduling

Leszek Gąsieniec·Benjamin Smith·Sebastian Wild
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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.

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Leszek Gąsieniec, Benjamin Smith, Sebastian Wild. 2021-11-02. Towards the 5/6-Density Conjecture of Pinwheel Scheduling. https://arxiv.org/abs/2111.01784

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