Minimizing Makespan and Preemption Costs on a System of Uniform Machines

Shachnai, Hadas; Tamir, Tami; Woeginger, Gerhard J.

doi:10.1007/3-540-45749-6_74

Cited by 13 publications

(16 citation statements)

References 14 publications

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“…This number of preemptions was shown to be optimal in the sense that there exist inputs for which every optimal schedule involves that many preemptions. This algorithm was later generalized and simplified for jobs of limited splitting constraints by Shachnai, Tamir and Woeginger [12]. In this paper we extend the ideas of [12] for general symmetric, convex and monotone target functions.…”

Section: Introductionmentioning

confidence: 96%

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Optimal Preemptive Scheduling for General Target Functions

Epstein

Tassa

2004

Lecture Notes in Computer Science

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We study the problem of optimal preemptive scheduling with respect to a general target function. Given n jobs with associated weights and m ≤ n uniformly related machines, one aims at scheduling the jobs to the machines, allowing preemptions but forbidding parallelization, so that a given target function of the loads on each machine is minimized. This problem was studied in the past in the case of the makespan. Gonzalez and Sahni [6] and later Shachnai, Tamir and Woeginger [12] devised a polynomial algorithm that outputs an optimal schedule for which the number of preemptions is at most 2(m − 1). We extend their ideas for general symmetric, convex and monotone target functions. This general approach enables us to distill the underlying principles on which the optimal makespan algorithm is based. More specifically, the general approach enables us to identify between the optimal scheduling problem and a corresponding problem of mathematical programming. This, in turn, allows us to devise a single algorithm that is suitable for a wide array of target functions, where the only difference between one target function and another is manifested through the corresponding mathematical programming problem.

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Section: Introductionmentioning

confidence: 96%

“…This algorithm was later generalized and simplified for jobs of limited splitting constraints by Shachnai, Tamir and Woeginger [12]. In this paper we extend the ideas of [12] for general symmetric, convex and monotone target functions. This general approach offers several benefits over the study of the particular makespan problem.…”

Section: Introductionmentioning

confidence: 96%

Optimal Preemptive Scheduling for General Target Functions

Epstein

Tassa

2004

Lecture Notes in Computer Science

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“…The paper [20] considered the generalized multiprocessor scheduling (GMS) problem, in which there is a total bound on the number of preemptions throughout a fea-sible schedule, and the goal is to find a schedule that satisfies the preemption constraint, such that the maximum job completion time (or, makespan) is minimized. The paper presents approximation schemes for identical and uniform machines.…”

Section: Related Workmentioning

confidence: 99%

Real-Time k-bounded Preemptive Scheduling

Albagli-Kim

Schieber

Shachnai³

et al. 2015

2016 Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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We consider a variant of the classic real-time scheduling problem, which has natural applications in cloud computing. The input consists of a set of jobs, and an integer parameter k ≥ 1. Each job is associated with a processing time, a release time, a due-date and a positive weight. The goal is to feasibly schedule a subset of the jobs of maximum total weight on a single machine, such that each of the jobs is preempted at most k times.Our theoretical results for the real-time k-bounded preemptive scheduling problem include hardness proofs, as well as algorithms for subclasses of instances, for which we derive constant-ratio performance guarantees. We bridge the gap between theory and practice through a comprehensive experimental study, in which we also test the performance of several heuristics for general instances on multiple parallel machines. We use in the experiments a linear programming relaxation to upper bound the optimal solution for a given instance. Our results show that while k-bounded preemptive scheduling is hard to solve already on highly restricted instances, simple priority-based heuristics yield almost optimal schedules for realistic inputs and arbitrary values of k.

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“…This algorithm runs in O(log n + log 3 m) time using n processors. Shachnai, Tamir and Woeginger [34] studied the problem of minimizing the makespan with preemption costs on a system of uniform machines scheduling. Pandelis [35] has considered the problem of scheduling independent jobs on uniform parallel machines.…”

Section: Offline Scheduling Of Preemptive Jobs Tomentioning

confidence: 99%

Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines

Panneerselvam¹,

Narayanan²

2010

IIM

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This paper presents a survey of single machine scheduling problem with uniform parallel machines. The single machine scheduling problem with uniform parallel machines consists of n jobs, each with single operation, which are to be scheduled on m parallel machines with different speeds. These parallel machines are also called proportional machines or related machines. There are several measures of performance which are to be optimized in uniform parallel machines scheduling. Since, this scheduling problem is a combinatorial problem; usage of a heuristic is inevitable to obtain solution in polynomial time. This paper gives a classification of the literatures of this scheduling problem in three major categories, viz. offline scheduling, online scheduling and miscellaneous scheduling. In total, the available literatures are classified into 17 subgroups. Under each of the first two categories, the available literatures are discussed under different groups based on different measures of performance and non-preemptive/preemptive nature of the jobs. In the last category, the literatures are discussed under three subgroups, namely non-preemptive jobs, preemptive jobs and periodic jobs.

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Minimizing Makespan and Preemption Costs on a System of Uniform Machines

Cited by 13 publications

References 14 publications

Optimal Preemptive Scheduling for General Target Functions

Optimal Preemptive Scheduling for General Target Functions

Real-Time k-bounded Preemptive Scheduling

Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines

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