Abstract

We consider the problem of minimizing the total flow time of a set of unit sized jobs in a discrete time model, subject to a temperature threshold. Each job has its release time and its heat contribution. At each time step the temperature of the processor is determined by its temperature at the previous time step, the job scheduled at this time step and a cooling factor. We show a number of lower bound results, including the case when the heat contributions of jobs are only marginally larger than a trivial threshold. Then we consider a form of resource augmentation by giving the online algorithm a higher temperature threshold, and show that the Hottest First algorithm can be made 1-competitive, while other common algorithms like Coolest First cannot. Finally we give some results in the offline case.

Highlights

  • In this paper we focus on the total flow time

  • No algorithm can give a bounded competitive ratio when hmax is allowed to be exactly R. This is because after scheduling any job with a nonzero heat contribution, any algorithm will forever have a positive temperature which means that it will never be able to schedule a job with heat R, and so such a job will end up with an infinite flow time

  • There are two possibilities: (1) If less than M B-jobs are scheduled in the T2-interval, i.e. at least M are delayed to after the big job, the total flow time of these B-jobs is at least (LN − 3M )M = L2M 2 − 3M 2 ≥ (L2/2)M 2 ≥ N 2/4, contradicting the condition of the lemma

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Summary

Introduction

This was shown to be strongly NP-hard in the offline case [7], even if all jobs have identical release times and identical deadlines They further showed that in the online case, all ‘reasonable’ algorithms are 2-competitive for R = 2 and this is optimal. Bampis et al [2] considered the objective of minimizing the makespan on m > 1 processors when all jobs are released at time 0 They presented a generic 2ρ-approximate algorithm using a ρ-approximate algorithm for classical makespan scheduling as a subroutine, and a lower bound of. We show a number of lower bounds as in the bounded job heat model; in particular we show that CF cannot be even constant competitive given any non-trivial higher threshold This is in stark contrast with the throughput case [7] where CF is optimal but HF can be shown to be not. Throughput the paper, R is assumed to be a constant whenever asymptotic notation is used

Preliminaries
Bounded Maximum Job Heat
1: A starts
Non-idling Algorithms
Rb can be made arbitrarily close
Increased Temperature Threshold
Lower Bound
Hottest First is 1-competitive
Inapproximability
Identical Release Times
Conclusion
Full Text
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