Brief Announcement: Nested Active-Time Scheduling

@article{Cao2022BriefAN,
  title={Brief Announcement: Nested Active-Time Scheduling},
  author={Nairen Cao and Jeremy T. Fineman and Shisheng Li and Juli{\'a}n Mestre and Katina Russell and Seeun William Umboh},
  journal={Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures},
  year={2022}
}
  • Nairen CaoJeremy T. Fineman S. Umboh
  • Published 11 July 2022
  • Business, Computer Science
  • Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures
The active-time scheduling problem considers the problem of scheduling preemptible jobs with windows (release times and deadlines) on a parallel machine that can schedule up to g jobs during each timestep. The goal in the active-time problem is to minimize the number of active steps, i.e., timesteps in which at least one job is scheduled. This paper presents a 9/5-approximation algorithm for a special case of the active-time scheduling problem in which job windows are laminar (nested). This… 

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References

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NP-completeness of the Active Time Scheduling Problem

This paper resolves this open problem and shows that the active time scheduling problem is indeed NP-complete.

Brief Announcement: A Greedy 2 Approximation for the Active Time Problem

A simple 2 approximation for the active time problem is given - a set of pre-emptible jobs, each with an integral release time, deadline and required processing length, which matches the state of the art bound obtained by a significantly more involved LP rounding scheme.

A Model for Minimizing Active Processor Time

This work presents a linear time algorithm for the case where jobs are unit length and each Ti is a single interval, assuming that jobs are given in sorted order and shows that the optimal non-preemptive schedule has active time at most 4/3 times that of the optimal preemptive schedule.

LP rounding and combinatorial algorithms for minimizing active and busy time

The preemptive busy time problem is considered, giving a simple and exact greedy algorithm when unbounded parallelism is allowed, i.e., g is unbounded, which yields an algorithm that is 2-approximate for arbitrary g.