Tightness Results for Malleable Task Scheduling Algorithms

Schwarz, Ulrich M.

doi:10.1007/978-3-540-68111-3_112

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…[24]). -One may also consider malleable jobs which can be assigned several machines and the actual processing time depends on the number of machines allocated (see e.g., [20], [24]). …”

Section: Summary Extensions and Future Workmentioning

confidence: 99%

Optimizing busy time on parallel machines

Mertzios

Shalom

Voloshin

et al. 2015

Theoretical Computer Science

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Abstract-We consider the following fundamental scheduling problem in which the input consists of n jobs to be scheduled on a set of identical machines of bounded capacity g (which is the maximal number of jobs that can be processed simultaneously by a single machine). Each job is associated with a start time and a completion time; it is supposed to be processed from the start time to the completion time (and in one of our extensions it has to be scheduled also in a continuous number of days; this corresponds to a two-dimensional version of the problem). We consider two versions of the problem. In the scheduling minimization version the goal is to minimize the total busy time of machines used to schedule all jobs. In the resource allocation maximization version the goal is to maximize the number of jobs that are scheduled for processing under a budget constraint given in terms of busy time. This is the first study of the maximization version of the problem. The minimization problem is known to be NP-Hard, thus the maximization problem is also NP-Hard. We consider various special cases, identify cases where an optimal solution can be computed in polynomial time, and mainly provide constant factor approximation algorithms for both minimization and maximization problems. Some of our results improve upon the best known results for this job scheduling problem. Our study has applications in power consumption, cloud computing and optimizing switching cost of optical networks.

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“…[24]). -One may also consider malleable jobs which can be assigned several machines and the actual processing time depends on the number of machines allocated (see e.g., [20], [24]). …”

Section: Summary Extensions and Future Workmentioning

confidence: 99%

Optimizing busy time on parallel machines

Mertzios

Shalom

Voloshin

et al. 2015

Theoretical Computer Science

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show abstract

“…In our problem, the cost of scheduling each of the jobs depends on the other jobs scheduled on the same machine in the corresponding time interval; thus, it may change over time and among different machines. Scheduling moldable jobs, where each job can have varying processing times, depending on the amount of resources allotted to this job, has been studied using classic measures, such as minimum makespan, or minimum (weighted) sum of completion times (see, e.g., [20,15] and a comprehensive survey in [19]). …”

Section: Related Workmentioning

confidence: 99%

Real-time scheduling to minimize machine busy times

Khandekar

Schieber

Shachnai

et al. 2014

J Sched

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ABSTRACT.We consider the following fundamental scheduling problem. The input consists of n jobs to be scheduled on a set of machines of bounded capacities. Each job is associated with a release time, a due date, a processing time and demand for machine capacity. The goal is to schedule all of the jobs non-preemptively in their release-time-deadline windows, subject to machine capacity constraints, such that the total busy time of the machines is minimized. Our problem has important applications in power-aware scheduling, optical network design and customer service systems. Scheduling to minimize busy times is APX-hard already in the special case where all jobs have the same (unit) processing times and can be scheduled in a fixed time interval. Our main result is a 5-approximation algorithm for general instances. We extend this result to obtain an algorithm with the same approximation ratio for the problem of scheduling moldable jobs, that requires also to determine, for each job, one of several processing-time vs. demand configurations. Better bounds and exact algorithms are derived for several special cases, including proper interval graphs, intervals forming a clique and laminar families of intervals. * Work partially supported by funding for DIMACS visitors.

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“…• One may also consider malleable jobs which can be assigned several machines and the actual processing time depends on the number of machines allocated (see e.g., [23,30]). …”

Section: Summary and Future Workmentioning

confidence: 99%

Online Optimization of Busy Time on Parallel Machines

Shalom

Voloshin

Wong

et al. 2012

Lecture Notes in Computer Science

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Abstract. We consider the following online scheduling problem in which the input consists of n jobs to be scheduled on identical machines of bounded capacity g (the maximum number of jobs that can be processed simultaneously on a single machine). Each job is associated with a release time and a completion time between which it is supposed to be processed. When a job is released, the online algorithm has to make decision without changing it afterwards. We consider two versions of the problem. In the minimization version, the goal is to minimize the total busy time of machines used to schedule all jobs. In the resource allocation maximization version, the goal is to maximize the number of jobs that are scheduled under a budget constraint given in terms of busy time. This is the first study on online algorithms for these problems. We show a rather large lower bound on the competitive ratio for general instances. This motivates us to consider special families of input instances for which we show constant competitive algorithms. Our study has applications in power aware scheduling, cloud computing and optimizing switching cost of optical networks.

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Tightness Results for Malleable Task Scheduling Algorithms

Cited by 5 publications

References 10 publications

Optimizing busy time on parallel machines

Optimizing busy time on parallel machines

Real-time scheduling to minimize machine busy times

Online Optimization of Busy Time on Parallel Machines

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