Towards the 5/6-Density Conjecture of Pinwheel Scheduling

by   Leszek Gasieniec, et al.

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.



There are no comments yet.


page 15


Compact Packings are not always the Densest

We provide a counterexample to a conjecture by B. Connelly about density...

Learning to solve the single machine scheduling problem with release times and sum of completion times

In this paper, we focus on the solution of a hard single machine schedul...

An EPTAS for machine scheduling with bag-constraints

Machine scheduling is a fundamental optimization problem in computer sci...

Fine-Grained Cryptanalysis: Tight Conditional Bounds for Dense k-SUM and k-XOR

An average-case variant of the k-SUM conjecture asserts that finding k n...

Collective Schedules: Scheduling Meets Computational Social Choice

When scheduling public works or events in a shared facility one needs to...

A Markov Chain Monte Carlo Approach to Cost Matrix Generation for Scheduling Performance Evaluation

In high performance computing, scheduling of tasks and allocation to mac...

Multiprocessor Global Scheduling on Frame-Based DVFS Systems

In this ongoing work, we are interested in multiprocessor energy efficie...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.